Astronomy
&
Astrophysics
A&A 572, A80 (2014)
DOI: 10.1051/0004-6361/201423551
c ESO 2014
Extending the supernova Hubble diagram to z ∼ 1.5
with the Euclid space mission
P. Astier1 , C. Balland1 , M. Brescia2 , E. Cappellaro3 , R. G. Carlberg4 , S. Cavuoti5 , M. Della Valle2,6 , E. Gangler7 ,
A. Goobar8 , J. Guy1 , D. Hardin1 , I. M. Hook9,10 , R. Kessler11,12 , A. Kim13 , E. Linder14 , G. Longo5 , K. Maguire9,15 ,
F. Mannucci16 , S. Mattila17 , R. Nichol18 , R. Pain1 , N. Regnault1 , S. Spiro9 , M. Sullivan19 , C. Tao20,21 , M. Turatto3 ,
X. F. Wang21 , and W. M. Wood-Vasey22
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LPNHE, CNRS/IN2P3, Université Pierre et Marie Curie Paris 6, Université Denis Diderot Paris 7, 4 place Jussieu,
75252 Paris Cedex 5, France
e-mail: [email protected]
INAF, Capodimonte Astronomical Observatory, via Moiariello 16, 80131 Naples, Italy
INAF–Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, 35122 Padova, Italy
Department of Astronomy and Astrophysics, University of Toronto, 50 St. George Street, Toronto ON M5S 3H4, Canada
Dept. of Physics, University Federico II, via Cinthia, 80126 Naples, Italy
International Center for Relativistic Astrophysics, Piazza Repubblica, 10, 65122 Pescara, Italy
Clermont Université, Université Blaise Pascal, CNRS/IN2P3, Laboratoire de Physique Corpusculaire, BP 10448,
63000 Clermont-Ferrand, France
Albanova University Center, Department of Physics, Stockholm University, Roslagstullsbacken 21, 106 91 Stockholm, Sweden
Department of Physics (Astrophysics), University of Oxford, DWB, Keble Road, Oxford OX1 3RH, UK
INAF–Osservatorio Astronomico di Roma, via Frascati 33, 00040 Monteporzio (RM), Italy
Department of Astronomy and Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA
Kavli Institute for Cosmological Physics, University of Chicago, 5640 South Ellis Avenue Chicago, IL 60637, USA
LBNL, 1 Cyclotron Rd, Berkeley CA 94720, USA
University of California Berkeley, CA 94720 USA
European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Garching bei München, Germany
INAF, Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy
Finnish Centre for Astronomy with ESO (FINCA), University of Turku, Väisäläntie 20, 21500 Piikkiö, Finland
Institute of Cosmology & Gravitation, University of Portsmouth, Portsmouth PO1 3FX, UK
School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ, UK
CPPM, Université Aix-Marseille, CNRS/IN2P3, Case 907, 13288 Marseille Cedex 9, France
Tsinghua center for astrophysics, Physics department, Tsinghua University, 100084 Beijing, PR China
PITT PACC, Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh PA 15260, USA
Received 31 January 2014 / Accepted 26 September 2014
ABSTRACT
We forecast dark energy constraints that could be obtained from a new large sample of Type Ia supernovae where those at high
redshift are acquired with the Euclid space mission. We simulate a three-prong SN survey: a z < 0.35 nearby sample (8000 SNe),
a 0.2 < z < 0.95 intermediate sample (8800 SNe), and a 0.75 < z < 1.55 high-z sample (1700 SNe). The nearby and intermediate
surveys are assumed to be conducted from the ground, while the high-z is a joint ground- and space-based survey. This latter survey,
the “Dark Energy Supernova Infra-Red Experiment” (DESIRE), is designed to fit within 6 months of Euclid observing time, with
a dedicated observing programme. We simulate the SN events as they would be observed in rolling-search mode by the various
instruments, and derive the quality of expected cosmological constraints. We account for known systematic uncertainties, in particular
calibration uncertainties including their contribution through the training of the supernova model used to fit the supernovae light
curves. Using conservative assumptions and a 1D geometric Planck prior, we find that the ensemble of surveys would yield competitive
constraints: a constant equation of state parameter can be constrained to σ(w) = 0.022, and a Dark Energy Task Force figure of merit
of 203 is found for a two-parameter equation of state. Our simulations thus indicate that Euclid can bring a significant contribution
to a purely geometrical cosmology constraint by extending a high-quality SN Ia Hubble diagram to z ∼ 1.5. We also present other
science topics enabled by the DESIRE Euclid observations.
Key words. cosmological parameters – dark energy
1. Introduction
Measuring distances to supernovae Ia (SNe Ia) at z ∼ 0.5
allowed two teams (Riess et al. 1998; Schmidt et al. 1998;
Perlmutter et al. 1999) to independently discover that the expansion of the Universe is now accelerating. The cause of this
acceleration at late times is still unknown and has been attributed to a new component in the Universe admixture: dark
energy. One can describe the acceleration at late times through
the equation of state of dark energy w (namely how its density
evolves with redshift and cosmic time), and the current results
are compatible with a static density, i.e. a cosmological constant
Article published by EDP Sciences
A80, page 1 of 20
A&A 572, A80 (2014)
(e.g. Betoule et al. 2014). Measuring precisely this equation of
state constitutes a crucial step towards understanding the nature
of dark energy (Albrecht et al. 2006; Peacock et al. 2006). Since
the discovery of acceleration, we have narrowed the allowed
region of parameter space, from SNe1 (e.g. Riess et al. 2004;
Astier et al. 2006; Riess et al. 2007; Wood-Vasey et al. 2007;
Kessler et al. 2009; Conley et al. 2011; Sullivan et al. 2011;
Planck Collaboration XVI 2014; Betoule et al. 2014; Sako et al.
2014), and also with other probes (e.g. Schrabback et al. 2010;
Blake et al. 2011; Riess et al. 2011; Burenin & Vikhlinin
2012; Planck Collaboration XVI 2014; Amati & Valle 2013).
Investigating the uncertainties of w measurements reveals that
distances to SNe are leading precision constraints. The current
constraints on a constant equation of state from a joint fit of
a flat w cold dark matter (wCDM) cosmological model to the
SN Hubble diagram and Planck cosmic microwave background
(CMB) measurements yields w = −1.018 ± 0.057(stat + sys)
(Betoule et al. 2014).
However, it is important to realise that in the quest for stricter
dark energy constraints, one should rely on several probes: different probes face different parameter degeneracies and efficiently complement each other; different probes are also subject
to different systematic uncertainties, and a cross-check is obviously in order for these delicate measurements. Both arguments
are developed in detail in Albrecht et al. (2006); Peacock et al.
(2006).
When one constrains cosmological parameters from distance
data, increasing the redshift span of the data efficiently improves the quality of cosmological constraints, and SN surveys
are hence targeting the highest possible redshifts. Cosmological
constraints from SNe derive from comparing event brightnesses
at different redshifts. For precision cosmology, one should aim
at comparing similar restframe wavelength regions at all redshifts, so that the comparison does not strongly rely on a
SN model. When aiming at higher and higher redshifts, groundbased SN surveys face two serious limitations related to the atmosphere: at wavelengths redder than ∼800 nm, the atmosphere
glow rises rapidly in intensity; this glow goes with large and
time-variable atmospheric absorption which makes precision
photometry through the atmosphere above 1 µm very difficult.
Cosmological constraints from SN distances are currently
dominated by distances measured in the visible, mainly at z <
∼ 1,
(e.g. Conley et al. 2011; Scolnic et al. 2014a; Betoule et al.
2014). The current sample of SN distances at z > 1 is dominated by events measured with NIR instruments (NICMOS and
WFC3) on the HST (Riess et al. 2007; Suzuki et al. 2012;
Rodney et al. 2012; Rubin et al. 2013) and amounts to less than
40 such events. These NIR instruments have a small field of view
compared to current ground-based CCD-mosaics. Extending the
Hubble diagram of supernovae at z >
∼ 1 with statistics matching
forthcoming ground-based samples at z <
∼ 1 requires NIR widefield imaging from space.
Euclid is an ESA M-class space mission, adopted in June
2012, which aims at characterising dark energy, from two main
probes (Laureijs et al. 2011): the spatial correlations of weak
shear, and the 3D correlation function of galaxies. The latter allows one to measure in particular the evolution of the expansion rate of the Universe by tracking the BAO peak as a function of redshift, while the study of the shear as a function of
redshift constrains both the expansion rate evolution and the
growth rate of structures. The growth rate of structures, and its
1
In this paper, SN and SNe mostly refer to Type Ia supernovae rather
than supernovae in a more general sense.
A80, page 2 of 20
evolution with redshift can also be probed by extracting redshift
space distortions from the envisioned 3D galaxy redshift survey.
Measuring both the expansion history and the growth rate evolution with redshift provides a new test of general relativity on
large scales because this theory predicts a specific relation between these two aspects. Alternative theories of gravity, which
might be invoked instead of dark energy, predict in general a
different relation between growth of structures and expansion
history (e.g. Lue et al. 2004; Linder 2005; Bean et al. 2007;
Bernardeau & Brax 2011; Amendola et al. 2013, and references
therein).
Euclid will be equiped with a wide-field NIR imager and is
hence well suited to host a high-statistics high-redshift supernova programme, aimed at extending the ground-based Hubble
diagram beyond z ∼ 1. This paper proposes such a SN survey
and evaluates the cosmological constraints it could deliver in association with measurements of distances to SNe at lower redshifts with ground-based instruments. An earlier paper (Astier
et al. 2011, A11 thereafter) aimed at designing a standalone
space-based SN survey and suggested a different route: it assumed that a Euclid-like mission could be equipped with a filter
wheel on its visible imager, which is no longer a plausible possibility within the adopted mission constraints. However, some
arguments developed in A11 still apply to the work presented
here and we will refer to this earlier study when applicable.
We present here a SN survey which addresses systematic
concerns and delivers valuable leverage on dark energy. The plan
of this paper is as follows: we will first discuss the requirements
of SN Ia surveys for high-quality distances (Sect. 2). We then
describe the salient points of our SN and instrument simulators
(Sect. 3). The proposed surveys are described in Sect. 4, and
the assumptions regarding redshifts and typing in Sect. 5. The
forecast methodology and the associated Fisher matrix are the
subjects of Sect. 6. Our results are presented in Sect. 7, and
we explore alternatives to the baseline surveys in Sect. 7.1. In
Sect. 8, we compare our findings to forecasts for the SN survey
projects within DES and WFIRST. We discuss issues related to
astrophysics of supernovae and their host galaxies in Sect. 9.
The data set we propose to collect with Euclid allows a wealth
of other science studies, and we present a sample of those in
Sect. 10. We summarise in Sect. 11.
2. Requirements for the supernova survey
Distances to SNe Ia rely on the comparison of supernova fluxes
at different redshifts. The evolution of distances (up to a global
multiplicative constant) with redshift encodes the expansion history of the Universe. We will now discuss various aspects of
the SN survey design intended to limit the impact of systematic
uncertainties.
One can summarise the current impact of systematic uncertainties on SN cosmology (Guy et al. 2010; Conley et al. 2011;
Sullivan et al. 2011, also known as SNLS3): the photometric
calibration uncertainties dominate by far over other systematics,
and contribute to the equation of state uncertainty by about as
much as statistics (see e.g. Table 7 from Conley et al. 2011). For
the latest SN+Planck results (Betoule et al. 2014), the calibration
uncertainties increase σ(w) from 0.044 to 0.057. There are, however, ways to reduce the impact of calibration uncertainties both
in the survey design, and in the calibration scheme. Regarding
the latter, adding new calibration paths (Betoule et al. 2013)
to the classical path via the Landolt catalogue (e.g. Regnault
et al. 2009) already reduced significantly the calibration uncertainty. Half of the current calibration uncertainty is due to
P. Astier et al.: Distances to high redshift supernovae with Euclid
0.03
Calibration
SNe Ia exhibit some variability both in light curve shape
and colour, both correlated with brightness (e.g. Tripp & Branch
1999, and references therein) and most SN distance estimators
rely in some way on these brighter-slower and brighter-bluer
relations. A common way of parametrising a distance modulus
µ ≡ 5 log10 (dL ), accounting for these relations is
Training statistics
σ(<µ>)
Colour smearing
0.02
µ = m∗B + α(s − 1) − βc − M,
0.01
m∗B ,
0
0.5
Redshift
1
Fig. 1. Contribution of various sources to correlated uncertainties, averaged over sliding ∆z = 0.2 bins for the SNLS3 analysis (data from
Guy et al. 2010). “Colour smearing” refers to the effect of uncertainties
of the band-dependent residual scatter model (see Sect. 3.3). The steep
increase at high redshift of this contribution and of that from SN model
training statistics are both due to those events being measured in bands
bluer in the rest-frame than the lower redshift events. We note that these
two contributions are indeed going down with sample size.
primary calibrators which is expected to decrease in the future.
The SNLS3 compilation is dominated at high redshift by the
SNLS sample, measured in the visible from the ground using
a camera that has limited sensitivity in its reddest band (i.e. the
z-band). This specific feature affects the precision of SNLS distances at z >
∼ 0.8, as discussed below. We discuss now how the
SN survey design can mitigate calibration uncertainties.
2.1. Wavelength coverage
If fluxes of SNe at different redshifts are measured at different
restframe wavelengths, one has to rely on some modelling of
the spectrum of SNe in order to convert relative fluxes to relative distances. Distances relying on such a model are affected
by systematic and statistical uncertainties from this model, correlating all events at the same redshift. This effect is illustrated
in the case of the SNLS survey by the Fig. 1, where one can
see that at the high-redshift end, uncertainties unrelated to the
measurement itself become important, especially because they
are common to all events. Because of the low sensitivity of the
imager in z band, these high redshift events are effectively measured in bluer restframe bands than events at lower redshifts,
which makes their distances sensitive to statistical and systematic uncertainties of the SN model. This SN model always derives from a training sample and inherits all uncertainties affecting this training sample. In particular, the calibration uncertainties affecting the SN model training sample propagate to these
distances to high-redshift events measured in restframe bands
extending bluer than U. So, a strategy requiring that all events
be measured in similar restframe bands reduces the impact of
SN model uncertainties on distances. We propose below a quantitative implementation of this requirement.
2.2. Amplitude, colour, and distance uncertainties
The signal-to-noise ratio (S/N) of the photometric measurements
affects the precision of distances, but at some point, distances
will not significantly benefit from deeper exposures. We discuss
here current intrinsic limitations of supernova distances as well
as how measurement precision contributes to distance precision.
(1)
m∗B
where
s, c are fitted SN-dependent parameters.
denotes
the peak brightness in restframe B filter, s is a stretch factor describing the light curve width (or decline rate), and c is a restframe colour most often chosen as B−V evaluated at peak brightness. α, β and M are global parameters derived from data (and
subsequently marginalised over), typically by minimizing the
distance scatter. They do not convey cosmological information,
but rather parametrise the brighter-slower, brighter-bluer and intrinsic brightness of SNe. For each event, the m∗B , s, c parameters are derived from a fit of a SN model to the measured light
curve points, in at least two bands, if colour is to be measured.
The m∗B and c parameters, which mainly determine the distance
precision, are derived from amplitudes of light curves in different bands, where “amplitude” refers to some brightness indicator
(e.g. the peak brightness) derived from the light curve in a single band. We will now discuss the requirements on the quality of
photometric measurements, and express those using amplitude
precision.
The contribution of the s uncertainty to the µ uncertainty is
sub-dominant for light curves spanning at least ∼30 restframe
days. On the contrary, since β turns out to be larger than 1 (for
c = B − V restframe, βB,V is indeed measured to be above 3,
see e.g. Guy et al. 2010), the c measurement uncertainty drives
the distance measurement uncertainty. Since the observed scatter of SNe distance moduli (given by Eq. (1)) around the Hubble
diagram is at best about 0.15 mag, c measurement uncertainties
above ∼0.04 mag will start to contribute significantly to the distance uncertainty. Figure 2 shows that the SNLS survey is within
this bound up to z = 1. This performance is however obtained on
a sample that is effectively flux-selected by spectroscopic identification, and that relies on the r band to measure colour at the
highest redshifts. This restframe UV region is affected by large
fluctuations from event to event (Fig. 4 of Maguire et al. 2012,
Fig. 8 of Guy et al. 2010). Worse, Fig. 4 of Maguire et al. (2012)
may suggest an evolution with redshift of the flux at wavelengths
shorter than 320 nm. So, we give up the rest-frame UV region
by requiring that filters with central wavelength below 380 nm
in the rest-frame are not used for distances. Amplitudes of light
curves in the BVR rest-frame region measured to a precision of
0.04 mag deliver a colour precision of about 0.045 mag with two
bands, and better than 0.03 mag with 3 bands. We note that measurements in the rest-frame UV, even if not used for distances,
are still available for photometric identification. Measurements
at ∼280 nm (rest frame) are available in certain redshift ranges,
and can be used as a possible control of evolution of supernovae,
as discussed in Sect. 9.2.
When a sizable fraction of the SN Ia population is lost at
the high-redshift end of the Hubble diagram because of flux selection, one has to simulate the unobserved events to correct for
the bias of the observed sample. This procedure aims at compensating for the so-called Malmquist bias, but the uncertainties
of such a procedure (see e.g. Wood-Vasey et al. 2007; Kessler
et al. 2009; Perrett et al. 2010; Conley et al. 2011; Kessler et al.
2013) limit the usefulness of an incomplete high redshift sample.
On top of possible systematics, there is a statistical price to pay:
an incomplete high redshift sample is on average bluer than the
A80, page 3 of 20
0.08
sig(LC amplitude)
color measurement uncertainty
A&A 572, A80 (2014)
Shot noise & intrinsic fluctuations
Shot noise only
0.06
0.04
0.15
0.1
SNLS-3 cosmology sample
g-band
r-band
i-band
z-band
0.05
0.02
0
0
0.5
1
z
Fig. 2. Measurement uncertainty of the c parameter in the SNLS survey
as a function of redshift, for events spectroscopically identified. Solid
circles show the contribution of the source shot noise alone, and the
squares include intrinsic fluctuations from event to event (also called
colour smearing). At z > 0.7, the shot noise contribution becomes essentially constant because the colour measurement relies on bluer and
bluer restframe bands, which are more and more sensitive to colour
changes. This might look favourable, but accounting for intrinsic fluctuations from event to event (squares), very large in the UV, swamps this
benefit. (Data obtained from fitting light curves from Guy et al. 2010.)
whole population, and induces correlations between β (Eq. (1))
and cosmological parameters2 which degrade the quality of cosmological constraints. Conversely, if the SN colour distribution
of the cosmological sample is the same at all redshifts, a wrong β
or even an inadequate form of the colour correction affects SNe
at all redshifts in the same way, and hence does not alter the average distance-redshift relation. So, all efforts need be made to
retain a very large fraction of the population at the highest redshift. Since high-redshift red SNe are very faint and thus missing
from SN samples, one can eliminate the potential bias by ignoring red events at all redshifts. The analyses typically reject both
blue and red events beyond 2.5 to 3σ (see e.g. Kessler et al.
2009; Conley et al. 2011) from the mean of the restframe B − V
distribution and the statistical cost is at the few percent level.
2.3. Light curve measurement precision requirements
We propose the following quality requirements for photometric
measurements of SNe Ia aimed at deriving distances:
1. We express the quality of light curve measurements from the
r.m.s uncertainty of their fitted amplitude. Our goal is to secure two bands measured to a precision of 0.04 mag and
a third band to 0.06 mag. Rationale: this ensures a colour
measured to 0.03 mag, such that the colour uncertainty is
sub-dominant in the distance uncertainty. As long as measurements meet this quality, there are no detection losses,
because detection and photometric measurements are carried
out from the same images. By discarding events at redshifts
2
From the distance modulus definition (Eq. (1)), one can infer that if
the average colour hci is independent of z, the average distance modulus hµi does not depend on β and hence estimates of cosmological
parameters and β are independent. In Kessler et al. (2013, Sect. 6.4), it
is shown that the value of β influences both the evaluation of Malmquist
bias and distance moduli in ways which tend to cancel each other on average. The statistical coupling between cosmological parameters and β
however remains.
A80, page 4 of 20
0
0
0.5
1
z
Fig. 3. Measurement uncertainties of fitted amplitudes of SNLS light
curves, propagating shot noise. The i-band precision is below 0.03 mag
up to z = 1, as well as the r-band up to z ' 0.75. SNLS observations rely
on thinned CCDs with a low QE in z-band. This band is thus shallow
and hence has a small weight in distances to high-redshift events. (Data
from fitting light curves from Guy et al. 2010.)
that do not meet these quality requirements, we effectively
construct redshift-limited surveys.
2. Do not use filters with central wavelength below 380 nm in
the restframe. Rationale: SNe Ia have large dispersions in the
UV, and there are indications of evolution below 330 nm.
3. Derive distances from most similar restframe regions at all
redshifts. To this aim, we only consider filters with central
wavelengths 380 < λ < 700 nm. Rationale: reduce dependence on SN model and its associated systematic (e.g. calibration of the training sample) and statistical uncertainties.
4. Measure light curves over [−10, +30] restframe days from
maximum light. Rationale: measure light curve width in order to account for the brighter-slower relation, and provide
light curve shape information for SN typing. Compare rise
and decline rates across redshifts for evolution tests.
These requirements will be used as guidelines for the SN survey
designs in Sect. 4. Figure 3 shows that the SNLS observations
meet these requirements up to z = 0.65; they fail at higher redshifts because of the modest sensitivity in z-band (the CCDs of
Megacam (Boulade et al. 2003) are optimised for blue wavelengths). An imager equipped with deep-depleted thick CCDs
can meet our requirements up to z ' 0.95, acquiring deep enough
y-band data, and with exposures significantly deeper than SNLS.
The strategy proposed for DES in Bernstein et al. (2012) does
not provide three bands redder than 380 nm at z >
∼ 0.68, because
it does not plan on using the low-efficiency y band.
Euclid hosts a visible imager, called VIS, equipped with a
single broad band 500 <
∼λ<
∼ 950 nm, in order to maximise the
S/N of galaxy shape measurements. Such a band corresponds
to merging two to three regular broadband filters. The requirements above exclude using this band for measuring distances to
SNe at z >
∼ 0.5, because at higher redshifts, it includes too blue
rest-frame regions. More generally, our requirement that measurements are similar across redshifts excludes an observer band
much wider than the others. However, deep Euclid visible data
of the SN hosts will be valuable for other reasons, discussed in
Sect. 10.
2.4. Cadence of the survey
In the above requirements, we have not discussed the sampling
cadence along the light curves because we have expressed the
depth requirement directly on the fitted light curve amplitude
(point 1). If an observing cadence meets this requirement, visits twice as frequent integrating half the exposure time will not
change significantly the precision of the fitted amplitude. As a
baseline, we adopt in what follows a four-day cadence in the observer frame, because this is more than adequate to sample light
curves of high-redshift supernovae and allows one to efficiently
study faster transients. We could measure distances to SNe Ia
using a somehow slower cadence, but with accordingly deeper
exposures at each visit.
3. Instrument and supernova simulators
3.1. Instrument simulator
In its current design, Euclid is equipped with a visible and a NIR
imager (Laureijs et al. 2011). The latter also has a slitless spectroscopic mode but what we will discuss here does not rely on
this capability, mainly because high redshift SNe are too faint for
slitless spectrocopy on Euclid to deliver a usable signal. We do
not rely either on the visible imager for measuring distances, as
mentioned above. Therefore, the SN observations we are going
to discuss rely solely on the NIR Euclid imager.
In order to assess the cosmological performance of possible surveys, we simulate SN observations in Euclid and other
imaging instruments. The first step is to evaluate the precision of
photometric measurements. For a given SED, observing setup
and observing strategy, our simulator computes the expected
flux and evaluates the flux uncertainty assuming measurements
are carried out using PSF photometry for a given sky background and detector-induced noise, and accounts for shot noise
from the source; this calculation is described in Appendix A.
For Euclid’s NIR imager, we use PSFs derived from full optical
simulations (including diffraction) and detector characteristics3 .
These optical simulations were used to define the exposure times
for NIR imaging in the Euclid observing plan for its core science. The most important parameters of our Euclid NIR imager
simulator are:
–
–
–
–
–
a mirror area of 9300 cm2 ;
a read-noise of 7 electrons;
a dark current of 0.1 electrons/pixel/s;
pixels subtend 0.300 on a side;
and the imager covers 0.5 deg2 on the sky.
This NIR imager has 3 bands (named y, J and H) roughly covering the [1−2] µm interval. The overall transmission of the imager bands (accounting for all optical transmissions and quantum efficiency of the sensors) are shown in Fig. 4. The important
parameters of the simulated photometry bands are provided in
Table 1.
We have used the zodiacal light models in space from Leinert
et al. (1998), more precisely the angular dependence from their
Table 16, and the spectral dependence from their Table 19. The
zodiacal light intensity depends on the ecliptic latitude because
of the albedo of solar system dust, and the darkest spots are
the ecliptic poles. Our Table 1 presents sky brightnesses at two
ecliptic latitudes. The brightest one, S 45 refers to 45◦ from the
3
We are in debt to R. Holmes for providing us with the PSFs, transmission curves displayed in Fig. 4 and sensor characteristics which allowed
us to simulate NIR imaging with Euclid.
Transmission
P. Astier et al.: Distances to high redshift supernovae with Euclid
0.45
0.4
0.35
0.3
0.25
0.2
y
J
H
0.15
0.1
0.05
0
10000
12000
14000
16000
18000
20000
Wavelength ( Å )
Fig. 4. Overall transmission of the 3 bands of the Euclid NIR imaging
system, in its current design. The H filter red cutoff has been pushed
to 2 µm compared to earlier designs. The cut-on of the y filter is determined by the dichroic that splits the beam between visible and NIR instruments.
Table 1. Characteristics of the Euclid bands simulated for the highredshift survey.
Band
y
J
H
λ̄
(nm)
1048
1263
1658
S 45
S 15
(AB/arcsec2 )
22.47 22.75
22.44 22.72
22.31 22.60
ZP
(mAB for 1e− /s)
24.03
24.08
24.74
NEA
(arcsec2 )
0.56
0.61
0.77
Notes. Columns include: central wavelength, sky brightness (in
AB magnitudes/arcsec2 ) at two separations from the ecliptic poles (45◦
and 15◦ ), zero-points (for AB magnitudes and fluxes in e− /s), and Noise
Equivalent Area (NEA) of the PSF (defined by Eq. (A.1)). This is the
area over which one integrates the sky background fluctuations when
performing PSF photometry for faint sources, accounting for pixelisation at 0.300 /pixel. The reported NEA values were averaged over source
position within the central pixel.
ecliptic pole where we assumed a zodiacal light flux density normalised to 7.54 × 10−19 erg/(cm2 s Å arcsec2 ) at 1.2 µm. With
this value, our simulator derives 5σ limiting AB magnitudes of
24.02, 24.03, and 23.98 for three exposures of 79, 81 and 48 s
in y, J and H respectively, assuming PSF photometry is carried
out. These values compare very well to the limiting magnitudes
of 24.00 (set by scientific requirements, see Laureijs et al. 2011)
found by the instrument development team, who indeed derived
the above exposure times of the “Euclid standard visit” that deliver this sensitivity.
Fields selected to monitor SN light curves have to be observable over long periods of time, and the Euclid spacecraft
design imposes that they are located near the ecliptic poles. We
will hence use in what follows the S 15 sky intensities from our
Table 1 which apply at 15◦ and closer to the ecliptic poles.
Our 5σ limiting magnitudes for 3 standard Euclid exposures
(79, 81, 48 s in y, J, H) then become 24.05, 24.07 and 24.03 in
y, J and H respectively, i.e. they are improved by ∼0.04 with
respect to 45◦ from the ecliptic poles. The improvement with
decreasing sky background is modest because read noise contributes ∼60 % to the total noise of the NIR standard Euclid
exposures.
3.2. Impact of finite reference image depth
Supernovae photometry is obtained by subtracting images without the supernova (deemed the reference images) from images
A80, page 5 of 20
A&A 572, A80 (2014)
with the supernova. Since the same SN-free images are subtracted from all light curves measurements, the SN fluxes along
the light curve are positively correlated, and have a larger variance than the fluxes before subtraction. This correlation and extra variance both vanish for an infinitely deep reference image,
but since we will not have an infinitely deep reference, the precision of light curve amplitude measurements is degraded with
respect to this ideal case. We detail in Appendix B the computation of the effect, and will come back later to its practical
implications.
Beyond the contribution to shot noise, differential photometry might also contribute to systematic uncertainties, especially
in the context of ground-based image sets with sizable variations of image quality. Tests on real images from a ground-based
SN survey (Astier et al. 2013) show that it is possible to obtain
systematic residuals below 2 mmag, hence negligible compared
with calibration uncertainties. The same tests show that the observed scatter of SN measurements follows the expected contributions from shot noise.
3.3. Supernova simulator
To simulate SNe Ia, we primarily made use of the SALT2 model
(Guy et al. 2007, 2010). This model is a parametrised spectral
sequence, empirically determined from photometric and spectroscopic data. We also made use of the brighter-slower and
brighter-bluer relations determined from the SNLS3 SN sample (Guy et al. 2010), and the average absolute magnitude MB =
−19.09 + 5 log10 (H0 /70 km s−1 /Mpc) in the Landolt (i.e. Vega)
system. Because of limitations of its training sample, SALT2
does not cover restframe wavelengths redder than 800 nm.
SALT2 parametrises events with 4 parameters: a date of
maximum light (in B-band) t0 , a colour c, a decline rate parameter X1 and an overall amplitude X0 . The latter is often expressed
as m∗B , the peak magnitude of the light curve in the redshifted
B-band. Given these parameters, a redshift and a luminosity distance, we can evaluate fluxes of the SN in the observer filter
at the required phase, and evaluate the uncertainty of the measurement, for the adopted instrumental setup and given observing conditions. Varying the cosmology only alters X0 (or m∗B ),
and in the simulations, we have assumed that the current uncertainties on the expansion history are now small enough to ignore the changes of measurement uncertainties when varying the
cosmology.
SALT2 does not assume any relation between brightness and
redshift. In the training process, the X0 of events are nuisance parameters. This allows one to decouple distance estimation from
light curve fitter training, and more importantly to train the light
curve fitter using data at unknown distance. Thus, the SALT2
trainings (Guy et al. 2007, 2010) use a mixture of nearby events
(including very nearby events where the redshift is a poor indicator of distance) and well-measured SNLS events. Since the
statistical uncertainty of the model eventually contributes to the
cosmology uncertainty, one has to minimise the former. In what
follows, we will emulate the LC fitter training in order to incorporate the uncertainties that arise from this process into the
cosmology uncertainties. We note that the light curve fitter training suffers from both statistical uncertainties (from the size and
quality of the training sample) and from systematic uncertainties
(typically the photometric calibration).
SALT2 is not a perfect description of SNe Ia, and there remain some variability of light curves around the best fit to data,
beyond measurement uncertainties. This scatter depends on the
adopted supernova model and was determined for SALT2 in
A80, page 6 of 20
Guy et al. (2010). The residual scatter is described there as a coherent move around the average model of all light curve points
of each band of each event, and it is found to depend on the restframe central wavelength of the band. This scatter is measured
to about 0.025 mag rms in BVR-bands and increases slowly towards red and very rapidly in the UV (Fig. 8 from Guy et al.
2010). This scatter (coined “colour smearing” in Kessler et al.
2009) is accounted for in the simulation, and causes the difference between the two sets of points in our Fig. 2. Kessler et al.
(2013) considers other colour smearing models than the SALT2
one and finds that this does not have a dramatic effect on the
recovered cosmology. We note that the sample size we are considering in this paper will allow us to considerably narrow down
the range of acceptable colour smearing models.
For the rate of SNe, we use the volumetric rate from Ripoche
(2008)
R(z) = 1.53 × 10−4 [(1 + z)/1.5]2.14 h370 Mpc−3 yr−1 ,
(2)
where years should be understood in the rest frame. Since these
measurements stop around z = 1, rates at higher redshifts were
assumed to become independent of z. These rates compare well
with the determination from Perrett et al. (2012). The rates proposed in Mannucci et al. (2007) (accounting for events “lost to
extinction”) yield a SN count (to z = 1.5) ∼25% larger than our
nominal assumption, with a similar redshift distribution. There
are determinations of SN Ia rates at z > 1 from the Subaru deep
field (Graur et al. 2011), and from the CLASH/Candels survey
(Graur et al. 2014; Rodney et al. 2014), which are compatible
with each other (see e.g. Fig. 1 of Rodney et al. 2014), and show
that our assumption of rates flattening at z = 1 is likely conservative at the 20 to 30% level. We will discuss later (Sect. 5.1) other
sources of uncertainty affecting the expected number of highredshift events and will eventually derive how the cosmological
precision depends on event statistics (Sect. 7.1). The redshift distribution of simulated events accounts for edge effects, i.e. we
reject events at the beginning or the end of an observing season
which do not have the full required restframe phase coverage.
The supernova simulation generates light curves in the userrequired bands, at the user-required cadence, on a regular (redshift, colour, stretch) grid. For each band of each event, we evaluate the peak fluxes and the weight matrix of the four event
parameters, by propagating the measurement uncertainty of all
measurement points in this band, accounting for the effect of
finite reference depth (Eq. (B.1)). These peak flux values and
weight matrices are used by a global fit (Sect. 6 below) which
will weight these events according to their redshift, colour and
decline rate using measured distributions from Guy et al. (2010).
The event weight also depends on the redshift-dependent SNe Ia
rate (Eq. (2)), the edge-effect corrected survey duration, and the
survey area. The colour smearing is accounted for during the
global fit.
4. Supernova surveys
The SNLS survey has delivered its three-year sample, together
with a cosmological analysis gathering the high quality SN
sample and accounting for sytematic uncertainties (Guy et al.
2010; Conley et al. 2011; Sullivan et al. 2011). This compilation amounts to about 500 well-measured events, and will grow
to about twice as much when SNLS and SDSS release their full
samples, and gathering the nearby samples (z < 0.1) that appeared recently (e.g Stritzinger et al. 2011; Hicken et al. 2012;
Silverman et al. 2012). Pan-STARSS1 has recently delivered a
Table 2. Depth of the visits simulated for the DESIRE survey.
Depth (5σ)
Exp. time (s)
i
26.05
700
z
25.64
1000
y
25.51
1200
J
25.83
2100
H
26.08
2100
Notes. Depth (5σ for a point source) and exposure times at each visit for
a 4-day cadence of the proposed DESIRE joint SN survey. The exposure
times for LSST i and z bands assume nominal observing conditions. For
Euclid NIR bands, the exposures times are the ones that would deliver
the required depth in a single exposure, if such long exposures are technically possible. The S/N calculations are described in Appendix A.
first batch of 112 distances to SNe Ia at 0.1 <
∼z<
∼ 0.6 (Scolnic
et al. 2014a; Rest et al. 2014), corresponding to 1.5 y of observations. The next significant increase in statistics is expected
from the Dark Energy Survey (DES), which aims at delivering ∼3000 new events in a 5-year survey extending to z ∼ 1.2
(Bernstein et al. 2012), to which we compare our proposal in
Sect. 8. To make significant improvements, a SN proposal for
the next decade should target at least 104 well-measured events
and should aim at significantly increasing the redshift lever arm.
4.1. High-z SN survey with Euclid: the DESIRE survey
As discussed in the introduction, measuring accurate distances to
SNe at z > 1 requires to observe from space in the NIR. With its
wide-field NIR capabilities, Euclid offers a unique opportunity
to deliver a large sample in this redshift regime. In this section,
we present the DESIRE survey (Dark Energy Supernova InfraRed Experiment) which will be a dramatic improvement in the
number of high quality SNe Ia light curves at redshifts up to 1.5.
Euclid observing time will be mostly devoted to a wide survey of 15 000 deg2 , with a single visit per pointing (Laureijs et al.
2011). Each single visit consists of 4 exposures for simultaneous visible imaging and NIR spectroscopy, and 4 NIR imaging
exposures of 79, 81 and 48 s in y, J and H respectively. We
refer to this set of observations as the “Euclid standard visit”.
The Euclid observing plan also makes provision for deep fields,
which consist of repeated standard visits, in particular in order
to assess the repeatability of measurements from actual repetition rather than from first principles. We attempted to assemble a
SN survey from these repeated standard visits and failed to find
a compelling standalone SN survey strategy. Our unsuccessful
attempts are described in Appendix C.
Since we aim at measuring 3 bands per event, and require
that these 3 bands map similar restframe spectral regions at all
redshifts, we need to observe in more than 3 observer bands in
order to cover a finite redshift interval. The obvious complement
to Euclid consists of i- and z-bands observed from the ground.
We identify at least three facilities capable of delivering these
observations: LSST (8 m, Ivezic et al. 2008), the Dark Energy
Camera (DECam) on the CTIO Blanco (4 m, Flaugher et al.
2010), and Hyper Suprime Cam (HSC) on the Subaru (8 m,
Miyazaki et al. 2012). The most efficient of these three possibilities is LSST; HSC would require about 3 times more observing time than LSST while DECam would require about 10 times
more. While these are all plausible options, we consider LSST
to be the most natural partner and we chose it to illustrate the
DESIRE survey in the remainder of this paper.
In Table 2, we display the depth per visit that delivers the required quality of light curves up to z = 1.5 (for an average SN).
This table also lists observing times derived using our instrument
rms of fitted peak magnitude
P. Astier et al.: Distances to high redshift supernovae with Euclid
0.08
z
0.06
i
y
J
0.04
H
0.02
0
0.8
1
1.2
1.4
1.6
z
Fig. 5. Precision of light curve amplitudes as a function of redshift for
the 5 bands of the DESIRE survey, assuming a 4-day cadence with the
exposure times of Table 2. To fulfill the requirements in Sect. 2.3, i-band
is used up to z = 1, z-band up to z = 1.2, and distances at z = 1.5
rely mostly on J- and H-band. For y, J and H bands, these calculations
assume a reference image gathering 60 epochs in Euclid.
simulator. For i and z band, we used the sensitivities used for
LSST simulations from Ivezic et al. (2008), however without accounting for the IQ degradation with air mass: somewhat longer
exposure times might be needed in order to reach the required
sensitivities. As for the Euclid observations, a slower cadence
could be accommodated provided the depth per visit is increased
accordingly. The derived precision of single-band light curve
amplitudes of average SNe Ia are displayed in Fig. 5. Examples
of simulated light curves are shown in Fig. 6.
We have assumed that Euclid could devote 6 months of its
programme to monitor this dedicated deep field, possibly within
an extended mission. The NIR exposure times in Table 2 add up
to 5400 s per visit and pointing. Monitoring 20 deg2 (40 pointings) at a four-day cadence uses 62.5% of the wall clock time for
integrating on the sky. The rest is available for overheads such
as readout, slewing, etc. Since building SN light curves require
images without the SN, the programme is split over two seasons
with identical pointings, so that each season, which consists of
45 visits, provides a deep SN-free image for the other season.
Thus, our baseline programme consists of two six-month seasons, where the SN survey is allocated half of the clock time.
In practice, this means that the same 10 deg2 field will be observed twice, in two 6-month seasons during which the field
should be visible from the ground. Within this scheme, the reference images (i.e. images without the SN) gather on average
1.5 observing season (i.e. 67 epochs for a 4-day cadence). We
accounted for the finite reference depth effect of Euclid images
assuming a 60-epoch reference (i.e. 1.3 season), following the
algebra provided in Appendix B. Regarding reference depth, the
situation for ground-based surveys is different since those are
planning 5 (for the DES SN survey, see Bernstein et al. 2012)
to 10 (for LSST, see Ivezic et al. 2008) observing seasons on the
same field. The effect then amounts to a less than 10% degradation of amplitude measurements due to shot noise, which is
sub-dominant in most of the redshift range, and we neglected
the effect.
Regarding light curves in Euclid bands, we varied the reference depth in order to assess the acceptable variations of this parameter, and we display the impact of different reference depths
in Fig. 7. Beyond 45 epochs (i.e. one season), the actual number
A80, page 7 of 20
z = 1.2
J-2
MAB
24
y-1
26
σ[Amp(Ne)]/σ[Amp(∞)]
A&A 572, A80 (2014)
y
J
2
H
Baseline
1.5
z
28
0
1
0
50
Observer days
z = 1.5
24
MAB
H-2
Fig. 7. Precision of light curve amplitude measurement, in units of the
measurement quality for an infinitely deep reference, as a function of
the number of epochs Ne used in the reference image. For each band,
the spread at a given reference depth is due to redshift (0.75 < z < 1.55),
and the effect increases with redshift. If all events were measured using
45 reference epochs (i.e. one season), the measurement precision would
degrade by less than 10% relative to the chosen baseline, i.e. 60.
Table 3. Simulated depths per visit of the LSST Deep Drilling Fields.
y
0
Observer days
50
Fig. 6. Simulated light curves of an average SN at z = 1.2 (top) and
z = 1.5 (bottom).
does not make a large difference with our baseline. On the contrary, scenarios with a reference shallower than 15 to 20 epochs
seriously degrade the measurement quality.
It is mandatory that the chosen field is observable by both
Euclid and a ground-based observatory. The former imposes a
field close to the ecliptic poles. The southern ecliptic pole suffers from Milky Way extinction and a high stellar density, but
there are acceptable locations within 10◦ from the pole, observable for 6 months or more from the LSST site. The amount of
observing time for LSST is modest, and could even be included
as one of its “deep-drilling fields”, which are already part of its
observing plan. DECam on the CTIO Blanco could likely deliver the required sky coverage and depth in less than a night
every 4th night. The northern ecliptic pole is observable by the
Subaru telescope.
4.2. Other SN surveys by the time Euclid flies
By the time Euclid flies, we expect that the Dark Energy Survey
(DES) will have produced a few thousand supernovae extending to z ∼ 1 (Bernstein et al. 2012). LSST is not constructed
yet, but it is expected to be a massive producer of SN light
curves in the visible. LSST can tackle two redshifts regimes.
First is the 0.2 <
∼ z <
∼ 1 regime already covered by ESSENCE
(Wood-Vasey et al. 2007), SNLS (Sullivan et al. 2011), and PanSTARSS (Scolnic et al. 2014a; Rest et al. 2014), and by DES in
the near future. Second is the “nearby” redshift regime, where
LSST’s large étendue and fast readout allow it to rapidly cover
A80, page 8 of 20
40
60
80
Ne : no. of epochs in reference
J-1
26
28
20
depth (5σ)
Exp. time (s)
g
26.47
300
r
26.35
600
i
25.96
600
z
25.50
780
y4
24.51
600
Notes. The exposure times refer to dark and otherwise average observing conditions. The y4 filter is the widest considered option for the
LSST y-band.
large areas of sky. We now sketch a plausible contribution of
LSST to the Hubble diagram of SNe Ia in these two redshift
regimes.
4.2.1. LSST deep-drilling fields
The LSST deep-drilling fields (DDF) observations cover several scientific objectives, including distances to SNe. The current
baseline for the observations consists of an approximately 4 day
cadence with exposure times provided in Table 3. The corresponding fitted amplitude precisions are displayed in Fig. 8. The
limiting redshift for a three-band measurement above 380 nm
(restframe) is z ' 0.95, where the quality of r-band is more than
adequate for identification. We note that the precisions displayed
in Fig. 8 leave a good margin for less-than-optimal observations:
a moderate degradation of image quality or time sampling would
not affect our conclusions.
The volume of LSST deep-drilling fields observations adequate for distances to SNe is not settled yet but the current goal
consists of monitoring 4 fields for 10 seasons. We conservatively
assumed the statistics corresponding to 4 fields (each of 10 deg2 )
monitored over five 6-months seasons. 5 fields over 4 seasons
yield the same event statistics.
4.2.2. Low-redshift supernovae with LSST
Cosmological constraints from relative distances enormously
benefit from a local measurement and essentially all cosmological constraints from the Hubble diagram of SNe Ia make use
rms of fitted peak magnitude
P. Astier et al.: Distances to high redshift supernovae with Euclid
0.06
Table 4. Main parameters of the simulated surveys.
y4
0.04
DESIRE
LSST-DDF
Low z
r
0.02
0
0.2
0.4
i
0.6
0.8
zmax
0.75
0.15
0.05
1.55
0.95
0.35
Area
(deg2 )
10
50
3000
Duration
(months)
2×6
4×6
6
Events
1740
8800
8000
Notes. The duration of the DESIRE survey is two times 6 months, but
the Euclid observations use only half of the clock time, and so add up
to 6 months of clock time.
z
g
zmin
1
z
Fig. 8. Precision of light curve amplitudes as a function of redshift for
the 5 bands of the LSST deep-drilling-fields survey, assuming a 4 day
cadence with the depths from Table 3. At the anticipated depth, the
contribution of the y4 band is marginal for distances to SNe. It however
provides us with 3 bands within requirements at the highest redshift.
of a nearby SN sample. Since the relative calibration between
surveys is currently a serious limitation (see e.g. Conley et al.
2011), we might wonder whether LSST itself might collect such
a nearby sample. The LSST wide survey is built from two 15 s
exposure visits (Ivezic et al. 2008), and covers 20 000 deg2 . The
depth required to measure the shear field and photometric redshifts for galaxies is eventually obtained from several hundred
exposures. If these exposures are evenly spread over 10 years,
the time sampling is too coarse to measure distances to SNe Ia.
We argue here that an uneven time sampling would allow us to
monitor some fields with a 4 day cadence within the same overall time allocation (and hence final depth): one or more seasons
observed at a ∼4-day cadence using the regular LSST observing
block (2 × 15 s) would deliver a depth per visit slightly higher
than the SDSS-II SN survey (Kessler et al. 2009; Sako et al.
2014). Since LSST aims at monitoring 20 000 deg2 for 10 years,
we conservatively assumed that a proper cadence for SNe might
be acquired over 3000 deg2 for 6 months, which amounts to
∼10 times the volume of the SDSS-II SN survey. We only consider events at 0.05 < z < 0.35 where the quality is safely within
requirements of Sect. 2.3. The lower redshift bound eliminates
worries about peculiar velocities significantly affecting redshifts.
The upper redshift bound derives from the cadence we have assumed and the depth of LSST visits. We note that this kind of
observing strategy is not adopted yet within LSST, although it is
actively studied. It might be implemented because it allows for
additional science that cannot be done with evenly distributed
sampling, and with no additional observing time.
The imposed quality requirements imply that all surveys are
able to detect many events beyond their assigned high-redshift
cutoff. This allows us to work in the redshift-limited regime in
order to capture a similar fraction of the SN population at all
redshifts. To summarise, we provide the main parameters for the
three surveys in Table 4.
5. Redshifts and SN classification
5.1. Redshifts
With the statistics we are considering, we cannot expect to classify spectroscopically all events entering the Hubble diagram,
as most of the SN surveys have done up to now. Spectroscopy
remains, however, the only way to acquire an accurate redshift,
and we will assume in what follows that host galaxy spectroscopic redshifts are acquired at some point, possibly after the
fact, using multi-object spectroscopy. The 4MOST and DESI
projects on 4 m telescopes would both be well suited to obtaining spectroscopic redshifts of the majority of the host galaxies,
as demonstrated by the sucessful use of the AAOmega instrument on AAT to observe host galaxies from SNLS (Lidman et al.
2013). Host galaxies remaining with unmeasured redshifts after
such a campaign would be followed up with optical and infrared
spectroscopy on 8 m or Extremely Large Telescopes.
In order to evaluate the required exposure times to acquire
host redshift with a multi-object spectrograph, and the efficiency
at obtaining host redshifts in SN surveys, we have studied how
spectroscopic redshifts were assigned to a subsample of the
SNLS events. We have selected SNLS spectra to 0.5 < z < 1,
which can be “translated” to 0.75 < z < 1.55 by multiplying
luminosity distances by 1.65, in order to emulate collection of
host redshifts in the DESIRE survey. We have examined 40 slit
spectra of “live” SNe collected using FORS2 on the VLT, and
the origin of redshift determination splits this “training” sample
into three event classes:
– 20 events happened in emission line galaxies (ELGs) where
the redshift was obtained from the [O ] doublet (3726
and 3729 Å, unresolved with FORS2). We have then measured the [O ] line intensity.
– 11 events happened in passive hosts and the redshift
was obtained from the Ca H& K absorption lines (3933
and 3968 Å). In these cases, we collected the host magnitudes from imaging data.
– 9 events did not have enough galaxy flux in the slit and were
assigned a redshift using supernova features.
We note that both the [O ] doublet and the Ca H&K lines remain within the wavelength reach of (deep-depleted) silicon sensors at z = 1.55. In order to derive exposure times at higher
redsdhifts than our SNLS subsample, we rely on the BigBoss
(now called DESI) proposal (Schlegel et al. 2009). Namely, this
proposal evaluates that with a 1000-s exposure time, it is possible to detect each member of the [O ] doublet at a S/N of
8 if the [O ] brightness is 0.9 × 10−16 erg/s, at a fairly extreme redshift of 1.75. Drawing from the SDSS experience, the
same proposal relates passive supernova magnitudes and the exposure time required to get a redshift. We have “translated” the
[O ] line brightnesses and host magnitudes of our test sample
to higher redshifts by increasing the luminosity distance by 1.65,
and using the BigBoss figures, we have evaluated that DESIRE
emission line host galaxies would require up to 300 ks to deliver
S /N = 8 per [O ] doublet member, and passive hosts would require up to 100 ks to deliver a redshift. Most of the hosts would
require significantly less. These derived exposure times compare
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A&A 572, A80 (2014)
well with the extrapolation of the typical ∼3600 s on FORS2 of
the SNLS spectra: this exposure time translates to ∼100 ks for
DESIRE host spectroscopy on DESI when accounting for the
mirror size ratio (∼22 for the diameter) and the fainter targets
(∼32 ). We find that the S/N requirement of the DESI proposal
for [O ] emitters is higher than the ones we obtained for the
faintest members of our training sample.
These exposure times might look large, but one should note
that in Lidman et al. (2013), exposure times of 90 ks are reported. The redshift reach of the Lidman et al. (2013) pioneering programme does not extend significantly at z > 1, because
it targeted hosts of SN candidates detected in the SNLS imaging data (Bazin et al. 2011), limited in redshift by the poor
red sensitivity of the Megacam sensors (see e.g. Boulade et al.
2003). One might also note that the ultra deep VIMOS survey
(50 ks exposures on the VLT) obtained a success rate at obtaining redshifts (Le Fevre et al. 2014) similar to our anticipation.
Regarding the [O ] line brightness of SN hosts, three features
indicate that our estimation is conservative; first, the SNLS spectroscopic campaign aimed at identifying live supernovae and the
slit position was firstly aimed at maximising the SN flux, with
less consideration for the host. Our training [O ] luminosities
are then likely to be underestimated, as compared to fibre-fed
spectroscopy targeting the host galaxy; second, the average [O ]
brightness of ELGs tend to increase with z, and SN hosts likely
follow this trend; third, as already mentioned, we are able to
measure host redshifts at S/N lower than 8 per [O ] doublet
member. So, we estimate that typically 75% of DESIRE host
redshifts could be secured by means of multi-fibre spectroscopy
in the visible. Fainter hosts could be targeted by more powerful instruments, and spectra of a subsample of the supernovae
themselves (Sect. 5.2) almost unavoidably deliver redshifts.
One might consider the possibility of relying on photometric redshifts of supernovae. These are now known to be significantly more accurate than photometric redshifts of host galaxies
(Palanque-Delabrouille et al. 2010; Kessler et al. 2010), thanks
to the homogeneity of the events. SN photometric redshifts however introduce correlated uncertainties between distance and redshift which would require a careful study. SN photometric redshifts also degrade the performance of photometric identification
and classification.
5.2. SN spectra
Spectra have been used to obtain detailed information on supernovae, mostly to empirically compare high- and low-redshift
spectra (e.g. Maguire et al. 2012, and references therein). We
can consider extending these comparisons to higher redshifts,
relying on future facilities: both ground-based extremely large
telescopes and the JWST will allow one to efficiently acquire
NIR good-quality spectra of SNe Ia at z ∼ 1.5 (Hook 2013).
Using the available Exposure Time Calculators, we have evaluated exposure times of 900 s for the E-ELT, and 1500 s for prism
spectroscopy using NIRSPEC on JWST to acquire a spectrum of
an average SN Ia at z = 1.55, with a quality sufficient to compare
spectral features with lower redshifts. We anticipate similar integration times with the 23 m Giant Magellan Telescope and the
(30 m) Thirty Meter Telescope. These integration times are significantly lower than the typical 2 h required to identify a z ∼ 1
SN Ia event using an 8 m class (ground-based) telescope.
In current surveys, SN spectra are primarily used to identify the events (see e.g. Howell et al. 2005; Zheng et al. 2008).
Although we cannot hope to reproduce this strategy, obtaining
SN spectra of a subsample will help characterise the transient
A80, page 10 of 20
population and in particular the interlopers of the Hubble diagram. Given the exposure times above, assuming 40 h per
semester awarded on both an ELT and JWST, and typically
30 mn per target including overheads, we could collect typically
300 live SN spectra. For the brightest targets, large programmes
on existing 8−10 m telescopes could deliver ∼200 spectra if
400 h could be gathered in total. So, collecting several hundred
spectra of DESIRE events is a plausible goal.
5.3. SN classification
Most core-collapse supernovae are fainter than SNe Ia, and exhibit a larger luminosity dispersion. In Sect. 3.5 of A11, following arguments developed in Conley et al. (2011), it is shown
that iteratively clipping to ±3σ the contaminated Hubble diagram yields acceptable biases to the distance redshift-relation,
under various contamination hypotheses. This crude approach
works because the contamination contribution to the Hubble diagram does not evolve rapidly with redshift. This crude typing
conservatively assumes that light curve shapes and colours do
not provide type information. Although all recent SN analyses
indeed clip their Hubble diagram, we regard this purification
through clipping as a backup plan, and we would prefer a selection based on colours and light curve shapes as proposed in e.g.
Bazin et al. (2011); Sako et al. (2011); Campbell et al. (2013).
The high photometric quality requirements we are imposing are
an obvious help in this respect. Any method used to purify the
Hubble diagram sample will be cross-checked using spectra of a
subsample of active SNe, see Sect. 9.2.
6. Forecast method
In order to derive cosmological constraints, we follow the methods developed for A11, with the aim of accounting as precisely
as possible for systematic uncertainties, including the interplay
between different uncertainty sources. We will discuss astrophysical issues associated with SNe Ia distances in Sect. 9, and
discuss here uncertainties mostly associated with the measurements themselves. In our forecast, we account for photometric calibration uncertainties, statistical light curve model uncertainties (because the training sample is finite), and photometric
calibration uncertainty of the training sample, residual scatter
around the model, fit of the brighter-slower and brighter-bluer
relations, and make some provision for irreducible distance errors. We account for systematic uncertainties using nuisance parameters, and build a Fisher matrix for all parameters (including SN event parameters) that we invert in order to extract the
covariance of the cosmological parameters. This gives us cosmological uncertainties marginalised over all other parameters.
The method is detailed in A11 and we list now the considered
uncertainty sources (and their size when applicable):
– The measurement shot noise.
– Statistical uncertainties of the light curve model. We assumed that it is trained on the cosmological data set.
– Systematic uncertainties due to flux calibration, both on SN
parameters and through the SN model training. Our baseline
assumes that the conversion of measured counts to physical
fluxes is uncertain at the 0.01 mag level rms, independently
for each band in visible and NIR. This level is conservative for the visible range considering the accuracy reached in
Betoule et al. (2013). The impact of varying the photometric
calibration accuracy is discussed in Sect. 7.1.
P. Astier et al.: Distances to high redshift supernovae with Euclid
– The intrinsic scatter of supernovae at fixed colour (called
colour smearing). We assign (magnitude) rms fluctuations
of broadband amplitudes of 0.025, following Fig. 8 of Guy
et al. (2010). We note that a more optimistic value σc = 0.01
was assumed in Kim & Miquel (2006). Larger smearings
are indeed observed in the UV, but we ignore bands with
λ̄ < 380 nm (where λ̄ is the central wavelength of the filter).
– We fit for both brighter-slower and brighter-bluer relations
and marginalise over their coefficients.
– We assume an intrinsic distance scatter of 0.12 mag, where
current estimates are around or below 0.10 (Guy et al. 2010).
The average Hubble diagram residual is about 0.14 rms,
where the difference to 0.12 is mainly due to colour
smearing.
– We assume that there is an irreducible distance modulus
error, affecting all events coherently, varying linearly with
redshift,
δµ = eM × z,
(3)
with a Gaussian prior σ(eM ) = 0.01. This distance modulus error accounts for possible evolution of SNe Ia with redshift, not accounted for by the distance estimator, which in
turn biases the measured distance-redshift relation. In A11
(Sect. 5.2), a metallicity indicator relying on UV flux is proposed that allows one to control the distance indicator at the
level of ∼0.01. Our ansatz above (Eq. (3)) makes provision
for δµ = 0.015 over the whole redshift range.
These uncertainties describe current know-how, in a rather conservative way. It is thus likely that we might eventually do better.
The code that implements the global fit successfully reproduces
the SNLS3 uncertainties.
In order to propagate uncertainties, we introduce nuisance
parameters in the fit (e.g. alteration to the photometric zero
points) and eventually marginalise over those. In order to emulate the light curve fitter training and the impact of calibration
uncertainties, event parameters are also fitted, together with offsets to the fiducial SN model. Appendix A of A11 compares the
propagation of uncertainties and the introduction of nuisance parameters and concludes that both approaches are strictly equivalent. Our global fit thus considers 5 sets of parameters:
– The event parameters in their SALT2 flavour: t0 is a reference date, X0 is the overall brightness, X1 indexes light curve
shape, and c is a rest-frame colour.
– The photometric zero points, or more precisely offsets to
their nominal values. We impose priors on these offsets
which account for photometric calibration accuracy, from
SN instrumental fluxes to physical fluxes.
– The global parameters (α, β, M) used to derive a distance
from the SN parameters:
µ = m∗B + αX1 − βc − M.
(4)
Following Eq. (3), we emulate an irreducible fully correlated
distance error with
M = M0 + eM × z,
(5)
where eM is constrained with a Gaussian prior of rms 0.01.
The actual parameters are hence (α, β, M0 , eM ). The overall
flux scale of the Hubble diagram is unknown and M0 , which
is marginalised over, accounts for it.
– The supernova model definition. We model both the peak
brightness of the average SN as a function of wavelength,
and how colour variations affect different wavelengths (see
Sect. 4.3.3 of A11). For both quantities we model offsets to
the fiducial SN model, using 10-parameter polynomials over
the SN model restframe spectral range, which makes more
than 2 parameters per regular broadband filter. These parameters account for the SN model training.
– The cosmological parameters.
SN cosmology usually proceeds in two steps: first extracting
event parameters by fitting a model to light curves, and then
fitting cosmology to distances derived from these event parameters. With calibration uncertainties at play, the first step results in
fully correlated event parameters, but the correlations due to systematics are in fact a small-rank matrix, compared to the number
of events we are considering here. Instead of this two-step procedure, we carry out both steps simultaneously summing all terms
in a single χ2 , where the light curve fit term also incorporates the
light curve fitter training. This method is equivalent to the twostep procedure but does not require propagating a large covariance or weight matrix between stages. The fit involves a large
number of parameters (more than 50 000) and the Appendix B
of A11 sketches the method used to compute the covariance matrix of a small subset of parameters, among which are the cosmological parameters.
7. Forecast results
In order to evaluate the cosmological constraints that the proposed surveys could deliver, we use the commonly used equation
of state (EoS) effective parametrisation proposed in Chevallier &
Polarski (2001): w(z) = w0 + wa z/(1 + z), and shown to describe
a wide array of dark energy models in Linder (2003). We define
the cosmology with two more parameters: ΩM the reduced matter density, and ΩX the reduced dark energy density, both evaluated today. Distances alone do not constrain efficiently these
4 parameters, and in practice, at least two external constraints
have to be added. We have settled for one CMB prior, taken
as a measurement of the shift parameter R ≡ Ω1/2
M H0 r(zCMB ),
and flatness. For the geometrical CMB prior, we compared the R
measurement to 0.32% (anticipated from Planck, see Mukherjee
et al. 2008, Table 1), with the binned w matrix for CMB alone
from Albrecht et al. (2009) projected on the (w0 , wa ) plane in
a flat Universe, and found extremely similar results. Both approaches take care to ignore information on dark energy from
the ISW effect in the CMB, because the latter concentrates on
large angular scales and might be difficult to extract. We also
wish to ignore the ISW effect in order to ensure a purely geometrical cosmological measurement that is insensitive to the growth
of structures after decoupling. The method also ignores potential
information from CMB lensing. We describe in Appendix E how
to obtain SN-only constraints from our results.
We simulate distances in a fiducial flat ΛCDM Universe with
ΩM = 0.27. We restrict the rest frame central wavelength of the
bands entering the fit to [380−700] nm, which leaves 3 to 4 bands
per event. Enlarging this restframe spectral range formally improves the statistical performance but breaks the requirement
that similar rest frame ranges are used to derive distances at all
redshifts.
The quality of EoS constraints are usually expressed, following Albrecht et al. (2006), from the area of the confidence contours in the (w0 , wa ) plane, and the normalisation
we adopt reads FoM = [Det(Cov(w0 , wa ))]−1/2 . Still following
A80, page 11 of 20
wa
low-z + LSST-DDF
+DESIRE
0.5
low-z + LSST-DDF
LSST-DDF+DESIRE
F.O.M (3 surveys)
A&A 572, A80 (2014)
205
0.7 0.75 0.8 0.85 0.9 0.95
fraction
200
0
1200
-0.5
1 1.05 1.1
1 σ contours
-1.2
-1.1
-1
-0.9
-0.8
w0
Fig. 9. Confidence contours (at the 1σ level) of the survey combinations
listed in Table 5. The assumptions for systematics correspond to the last
row of Table 6.
1400
1600
1800
2000
Total Number of DESIRE supernovae
Fig. 10. FoM for the 3 surveys as a function of the SN statistics in
DESIRE. The upper horizontal scale is the fraction of events actually
entering into the Hubble diagram, with respect to our baseline assumptions. Event rate measurements at z > 1 (see Sect. 3.3) suggest higher
statistics (by ∼20%) than we assumed, and the efficiency at getting host
redshifts could eliminate 25% of the events. In any case, we see that the
cosmological performance does not depend critically on these numbers.
Table 6. Cosmological performance with various uncertainty sources.
Table 5. Cosmological performance of the simulated surveys.
low-z + LSST-DDF
+ DESIRE
low-z + LSST-DDF
LSST-DDF + DESIRE
σ(wa )
zp
σ(w p )
FoM
0.22
0.25
0.022
203.2
0.28
0.40
0.22
0.35
0.026
0.031
137.1
81.4
Notes. The FoMs assume a 1D geometrical Planck prior and flatness.
z p is the redshift at which the equation of state uncertainty reaches
its minimum σ(w p ). The FoM is defined as [Det(Cov(w0 , wa ))]−1/2 =
[σ(wa )σ(w p )]−1 and accounts for systematic uncertainties. The contributions of the main systematics are detailed in Table 6.
Albrecht et al. (2006), we define the pivot redshift z p to be where
the EoS uncertainty is minimal, and w p ≡ w(z p ). σ(w p ) is also the
uncertainty when fitting a constant EoS. σ(w p ) can be regarded
as the ability of the proposed strategy to challenge the cosmological constant paradigm. In Table 5, we report the following
performance indicators: σ(w p ), the uncertainty of the EoS evolution σ(wa ), and the FoM. The FoM difference between the two
first lines shows the Euclid contribution to the overall FoM: by
delivering about 10% of the total event statistics (see Table 4),
the high redshift Euclid part of the Hubble diagram increases
the FoM by ∼50%. The confidence contours corresponding to
Table 5 rows are displayed in Fig. 9.
We present in Table 6 some combinations of uncertainties,
and we find (as in Table 5 of A11) that the dominant reduction
in the figure of merit arises from the combination of calibration
uncertainties and SN model training. In A11, we also considered
the impact of several hypotheses such as fitting the α and β parameters (Eq. (4)) separately in redshift slices, or assuming that
there are several event species, each with its light curve model
and (α, β, M0 , eM ) set, and concluded that these extra parameters
result in negligible degradation of the cosmological precision.
The event statistics of the DESIRE survey is primarily limited by the amount of time available on Euclid, and is hence
A80, page 12 of 20
Assumptions
cal evo train
n
n
n
y
n
n
n
y
n
y
y
n
n
n
y
n
y
y
y
n
y
y
y
y
σ(wa )
0.15
0.18
0.18
0.20
0.16
0.18
0.21
0.22
zp
0.30
0.30
0.25
0.27
0.30
0.25
0.28
0.25
σ(w p )
0.016
0.016
0.018
0.019
0.016
0.018
0.020
0.022
FoM
418
339
315
266
403
304
238
203
Notes. “cal” refers to calibration uncertainties (σZP = 0.01). “evo”
refers to evolution systematics (Eq. (3)). “train” refers to SN model
training from the same sample.
not extensible. It is then important to assess the impact of lower
statistics on the cosmological performance. We remind here that
rates at z > 1 are uncertain (but we have adopted a conservative approach), and that we have evaluated that a massively parallel spectroscopic campaign to collect DESIRE host redshifts
could reasonably target a ∼75% completion rate (see Sect. 5.1).
We show in Fig. 10 that the cosmological performance is not
severely affected by a significant decrease of the DESIRE event
statistics actually entering into the Hubble diagram.
7.1. Altering the baseline survey and systematic hypotheses
The photometric calibration uncertainty (i.e. the zero point uncertainty) and the evolution uncertainty (Eq. (5)) constitute the
two main performance drivers with a fixed SN sample size.
Fig. 11 shows the cosmological performance as a function of
the size of these systematic uncertainties. Regarding the photometric calibration, we have varied only the NIR calibration
accuracy (i.e. Euclid’s photometric calibration), since photometric calibration accuracy in the visible is already better than
what we assumed (see Betoule et al. 2013). We note that the
P. Astier et al.: Distances to high redshift supernovae with Euclid
0.03
σZP(Euclid only)
Table 7. Effect of altering some survey parameters.
visible :
σZP = 0.01
σ(wp) = 0.026
Alteration
none
statistics (all surveys) × 1.25
statistics (all surveys) × 0.75
low-z × 1.25
low-z × 0.75
LSST-DDF × 1.25
LSST-DDF × 0.75
DESIRE × 1.25
DESIRE × 0.75
σc = 0.015
σint = 0.10
σc = 0.04 σint = 0
0.024
0.02
0.022
0.01
0.020
0
0.01
0.02
0.03
σ(e )
M
σZP(Euclid only)
0.03
visible :
σZP = 0.01
200
230
0.01
0
FOM = 140
170
0.02
260
0
FoM
203
231
172
218
187
212
193
208
199
223
231
204
Notes. σc refers to colour smearing (0.025 by default), σint refers to the
Hubble diagram scatter (without any shot noise nor colour smearing),
set to 0.12 in our baseline.
0.018
0
σ(w p )
0.022
0.021
0.024
0.022
0.023
0.022
0.023
0.022
0.022
0.021
0.021
0.022
0.01
0.02
0.03
σ(e )
M
Fig. 11. Contour levels of σ(w p ) (top) and the FoM (bottom) as a function of Euclid calibration accuracy σZP (equal for all Euclid filters), and
the distance evolution uncertainty σ(eM ) (defined in Eq. (5)). The stars
indicate our baseline (0.01, 0.01). One can note that significantly worse
hypotheses do not dramatically degrade the capabilities of the proposed
surveys.
performance is reasonably robust to significant changes in these
two uncertainties.
We investigate how the performance varies with statistics in
Table 7: the FoM varies roughly as the square root of the total number of events (rather than linearly without systematics
nor external priors). By altering the overall statistics of each of
our three surveys separately, we show that all three contribute
similarly to the cosmological precision (as already indicated in
Table 5). The DESIRE part shows the smallest relative change,
mostly because it has the smallest number of events in a first
place. We note that modest improvements of the SN modelling
quality (intrinsic scatter and colour smearing) significantly improve the overall performance.
Scolnic et al. (2014b) propose to describe the scatter around
the brighter-bluer relation using σc = 0.04 and σint = 0, where
we use by default respectively 0.025 and 0.12; transferring the
scatter from brightness to colour also increases β from 3 to ∼4.
With this extreme setup, we find a FoM of 204, i.e. unchanged
with respect to our baseline.
Rather than altering globally the statistics of the three proposed surveys, one may study how a small event sample at a
given redshift improves the cosmological performance as a function of this redshift. With our setup, z < 0.1 is the most efficient redshift range, because we have less than 200 events at
0.05 < z < 0.1 (see Fig. 12). Adding 200 supernovae at z =
0.05 improves the figure of merit by more than 30. However, incorporating a low-redshift sample into the analysis requires that
it is measured in three bands in the B, V, R spectral region, that
the photometry is precisely cross-calibrated with respect to other
samples and that this nearby sample is essentially unbiased. The
latter probably implies to collect it in the “rolling search” mode,
which is a demanding requirement given the sky area that has
to be patrolled for collecting 200 low-redshift SNe Ia. We have
not incorporated such a sample in our forecast, but one could argue that existing facilities (e.g. PTF Law et al. 2009; Skymapper
Keller et al. 2007) could deliver it soon.
8. Comparison with the DES and WFIRST
SN survey proposals
Bernstein et al. (2012) present the forecasts for a SN survey
to be conducted within the Dark Energy Survey (DES). This
work anticipates about 3000 events with acceptable distances at
0.3 < z < 1.2, complemented by a 300-event nearby sample and
500 events from the SDSS. The presented cosmological constraints incorporate a “DETF stage-II prior” 4 , which accounts
for more than just Planck constraints: on its own, this prior delivers a FoM of 58. The forecast does not account for uncertainties arising from SN model training. In order to compare our
findings with this work, we compute our FoM in the same conditions: we temporarily adopt the same external prior, we ignore
SN model training uncertainties, and we let the curvature float.
4
We are grateful to R. Biswas for providing us with the weight matrix
of this prior.
A80, page 13 of 20
Events per ∆ z = 0.1
A&A 572, A80 (2014)
Table 8. Our findings for the WFIRST SN survey performance, complemented by 800 nearby events.
low-z
(LSST Shallow)
Assumptions
LSST DDF
cal
n
y
n
y
n
n
y
y
3
10
DES 5
DESIRE
DES 10
2
10
SDSS
0.5
1
1.5
Redshift
Fig. 12. Redshift distribution of events for various surveys. For the
SDSS and SNLS, the distributions sketch the total sample of spectroscopically identified events eventually entering the Hubble diagram.
“DES 5” and “DES 10” refer respectively to the “hybrid-5” and
“hybrid-10” strategies studied in Bernstein et al. (2012), where the baseline is hybrid-10. “LSST-SHALLOW”, “LSST-DDF” and “DESIRE”
refer to the three prongs studied in this proposal.
Our assumptions about calibration uncertainties are already the
same as those from Bernstein et al. (2012). We find a FoM
of 468 for our 3 surveys, to be compared to 124 for the SN DES
survey (Bernstein et al. 2012, Table 15). It is hence clear that our
proposal constitutes a significant step forward after DES. We
compare the redshift distributions of the DES planned observations with the current samples and our proposal in Fig. 12.
WFIRST is a NASA project of a NIR wide-field imaging
and spectroscopy mission in space (Green et al. 2012, W12
hereafter). The mission is presented in two versions DRM1 and
DRM2 with mirrors of 1.3 and 1.1 m diameter and durations of
5 and 3 years respectively. In both instances, the primary mirror
is un-obstructed, which not only enhances its collecting power,
but also allows for a more compact PSF than a conventional onaxis setup with the secondary mirror and its supporting structure
in the beam. The baseline supernova survey (assuming DRM1,
see W12 p. 34) makes use of 6 months of observing time spread
over 1.8 y, and devotes more than two thirds of its observing time
to low-resolution prism spectroscopy; the remainder is used for
imaging in J, H and K bands every 5 days. This is a dual-cone
survey, where the deep part targets 0.8 < z < 1.65 and covers 1.8 deg2 , and the shallow part targets z < 0.8 over an area
of 6.5 deg2 , to which one should add the contribution from the
deep survey footprint. The integrations at each visit last 1500 s
and 300 s in the two surveys. The forecast adds a nearby survey of 800 events (at typically z < 0.1). We thus have three
redshift regimes which roughly gather (in increasing order) 800,
1400 and 700 events. The high-z part gathers about half of the
statistics targeted by DESIRE, but extends to higher redshifts.
The low-redshift part is very different from the one we have
sketched: it is first at lower redshift and second should be measured in significantly redder bands (around 1 µm) than most current nearby samples (and our projected low-z part), in order to
A80, page 14 of 20
train
n
n
n
n
y
y
y
y
σ(wa )
0.19
0.24
0.22
0.26
0.32
0.34
1.04
1.05
zp
0.28
0.37
0.24
0.32
0.32
0.30
0.33
0.33
σ(w p )
0.016
0.025
0.019
0.029
0.017
0.021
0.032
0.035
FoM
323
170
242
132
180
137
30
28
Notes. “cal” refers to calibration uncertainties (σZP = 0.01). “evo”
refers to evolution systematics (Eq. (3)). “train” refers to SN model
training from the same sample. The same quantities for our proposal
are shown in Table 6.
SNLS
0
evo
n
n
y
y
n
y
n
y
match the restframe bands of higher redshift events considered
in the project. The intermediate part is also very different from
our LSST-DDF sketch (or any ground-based z < 1 SN survey
in the visible) because it measures in the NIR. It is not obvious that the project would significantly benefit from considering intermediate-redshift events measured in the visible from the
ground, and the forecast concentrates on an essentially spacebased programme.
The anticipated sensitivity of the instrument outperforms
Euclid by more than 0.7 mag: a 1500 s integration with WFIRST
reaches beyond H = 26.7 (5σ point source)5 while Euclid remains below H = 26 (despite its wider H filter). The chosen
strategy makes a very efficient use of this exquisite sensitivity
by acquiring low-resolution spectra of all space-based events,
which is not a plausible option for Euclid. The quality requirement for light curves is slightly stricter than ours: S /N > 15 at
maximum light with a 5 day-cadence, while ours translates to
S /N > 12 at maximum for the same cadence. The WFIRST survey design breaks our requirement regarding similar restframe
wavelengths at all redshifts, because the span of the measurements in (J, H, K) (about a factor of 2 in wavelength) is narrower
than the redshift range 0.1 < z < 1.65 (i.e. 1 + z varies by about
2.4). Relative distances hence heavily rely on the SN model and
are affected by calibration uncertainties of the training sample.
In W12, systematic uncertainties of distances to SNe are modelled as independent in ∆z = 0.1 bins with a value that matches
the statistical accuracy from ∼50 events in the same bin at low
redshift and ∼25 events at high redshift. With these assumptions
and Planck priors, W12 find a FoM of about 150, which reaches
240 when systematic uncertainties are halved. The z > 1.5 part
contributes less than 20 to the FoM (Fig. 18 of W12).
In order to compare the SN survey proposed in W12 to
the present proposal, we apply our simulator to the WFIRST
SN survey, in particular with our baseline systematic uncertainties. We have thus performed an approximate simulation
of the 3-prong survey proposed in W12, and we note that we
are in a regime where intrinsic fluctuations dominate over shot
noise, and hence the details of the instrument sensitivity are
not crucial. With our assumptions about rates, we find similar
overall statistics to W12, larger for the high-z part by about
200 events, and lower for the mid-z part by the same amount.
We do not regard this difference as important. Table 8 displays
5
We computed the anticipated depth of a 1500 s SN visit from the
reported depth H = 29.6 of the final stack of ∼130 epochs (W12, p. 10).
P. Astier et al.: Distances to high redshift supernovae with Euclid
the cosmological performance we extract from our simulator,
which is again strongly driven by assumptions about systematics
at play. When considering uncertainties induced by photometric
calibration and evolution, we find a FoM of ∼130, very close to
the value of ∼150 found in W12, although we have assumed that
uncertainties are correlated across redshifts. Because the restframe wavelengths are changing with redshift, the SN model
cannot be extracted from the same sample, as indicated by the
dramatic performance drop in the last rows of Table 8. For the
proposed SN survey of W12, the observed SN fluxes as a function of redshift can be described by different associations of an
SN model (i.e. flux as a function of wavelength) and a distanceredshift relation, and extracting both from the data yields large
cosmological uncertainties. These large uncertainties motivate
our strategy of extracting distances from the same rest-frame region at all redshifts. The projections in W12 assume, in contrast
to ours, that the SN model has been developed elsewhere, and
that the assumed systematic uncertainties make provision for all
SN model uncertainties. For our proposal, we get a FoM = 266
if we ignore SN model uncertainties (see Table 6).
Recently, a new WFIRST concept has been proposed, relying on an existing 2.4m space-quality on-axis primary mirror. A
scientific programme and an instrument suite taking advantage
of this powerful telescope have been proposed (Spergel et al.
2013). The supernova programme still uses 6 months of observing time but follows a different route: SNe are discovered using
the wide-field imager and their distance are estimated from a
series of photometric R ∼ 100 spectra (0.6 < λ < 2 µm) obtained using an Integral Field Unit. The SN programme acquire
∼7 spectra of the SN at a 5-day cadence, and the equivalent of
4 epochs for the reference. The SN spectra deliver a S/N for
synthetic broad-band photometry of about 15 per filter at each
visit, except for one spectrum at maximum light that reaches
S /N ' 50. Events are selected for spectro-photometric followup so that the redshift distribution is flat at 0.6 < z < 1.7 with
136 events per ∆z = 0.1, and more populated at lower redshifts.
The forecast anticipates similar contributions of systematics and
statistics, using the optimistic hypothesis for systematics from
W12: the IFU instrument is assumed to be easier to calibrate
than an imager, and using spectroscopy allows one to get rid of
cross-redshift K-corrections. The forecast does not provide a figure of merit. It seems a priori very difficult to complement the
proposed analysis using samples measured in the visible from
the ground through imaging (as in our sketch), both because of
the different measurement technique but also because of the different restframe wavelength coverage.
Both SN proposals for WFIRST aim at covering a redshift
range wider than the spectral coverage of the instrument, and
hence have to measure supernovae at different redshifts in different restframe spectral ranges. This makes both of them vulnerable to inaccuracies of the SN model used to relate these different restframe spectral regions. To get around this limitation,
one either has to show that the incured uncertainties are negligible (our Table 8 indicates that it is not the case), or narrow the
redshift range of the space project to match the wavelength coverage of the instrument. In this second hypothesis, all considered
NIR space missions will have to complement their high-redshift
samples with lower redshift events presumably from wide-field
ground-based facilities.
Regarding the 2.4 m supernova survey project, it still has
to be demonstrated that measuring flux ratios from an IFU can
reach the required accuracy (typically a few 10−3 ). On the other
hand, one cannot question that a 2.4 m wide-field space mission has a farther reach than Euclid for distances to SNe, should
it eventually rely on the “traditional” and established imaging
methods. The time line of this project remains uncertain.
9. Astrophysical issues
9.1. Host galaxy stellar mass
It has been shown that even after applying the brighter-slower
and brighter-bluer relations, residuals of the Hubble diagram
are correlated with host galaxy stellar mass (Kelly et al. 2010;
Sullivan et al. 2010; Lampeitl et al. 2010). Obviously, the host
galaxy stellar mass is a proxy for some physical source of the
effect yet to be uncovered (see e.g. Gupta et al. 2011; Childress
et al. 2013), possibly metallicity (D’Andrea et al. 2011; Hayden
et al. 2013; Pan et al. 2013). In the first analyses considering
this effect, ignoring it caused a sizable bias on w (e.g. about
0.08, Sullivan et al. 2011), mostly because low-redshift searches
favour massive hosts, while rolling searches discover events regardless of the host properties. The “JLA” SN sample (Betoule
et al. 2014) is composed at more than 80% by the SDSS and
SNLS rolling searches, and when fitted together with Planck,
ignoring the host mass dependent brightness shifts w by less
than 0.01. This does not conflict with the 5σ detection of the
host mass dependent brightness on this sample, but rather indicates that its host mass distribution evolves slowly with redshift.
In the PS1 SN analysis (Scolnic et al. 2014a), the host-mass effect turns out to be barely detected.
The required host stellar mass precision is modest because
the correction varies slowly with stellar mass (e.g. Fig. 3 of
Sullivan et al. 2010). This host stellar mass is estimated using
galaxy population synthesis models fitted to broad-band photometric measurements of host galaxies. As in past SN surveys,
the surveys we are discussing in this paper offer the opportunity
to gather this photometric data in typically 5 bands. Although
it is likely that our understanding of the phenomenon will have
improved by the time Euclid flies, the data required to account
for the effect by current methods is indeed a by-product of the
SN surveys, as experienced by current projects. The photometric depth obtained by stacking all DESIRE images (Sect. 10.2)
seems sufficient for this purpose, considering that, as done currently, one can just assign a low stellar mass to apparently hostless SN events.
As discussed above and in A11, if the understanding of the
effect requires separate models for SN subclasses, and/or separate α, β, and M for different stellar mass hosts, or some other
quantity, as suggested in Hayden et al. (2013), the degradation
of cosmological performance is negligible.
If obtaining host redshifts significantly selects among the
event population (in particular in the DESIRE part), the analysis should take care at restoring similar host populations at all
redshifts, typically in order to ensure that applying or not the
chosen host correction does not have a serious effect on cosmological conclusions. This might in turn reduce the statistics of
nearby and mid-redshift samples. For these samples, one should
regard the event statistics we have considered as what is actually used for cosmology. We note that for both of these samples,
our hypotheses are well below what the LSST instrument can
plausibly deliver within its planned programme.
9.2. Spectroscopy of “live” supernovae and metallicity
diagnostics
Almost all SN cosmology works so far have acquired a live spectrum of their events, but this is impractical for the sample size we
A80, page 15 of 20
A&A 572, A80 (2014)
are considering here. We however still envisage collecting a sizable sample of SN+host spectra. This is known to be feasible at
z < 1 (e.g. Zheng et al. 2008; Balland et al. 2009; Blondin et al.
2012). In the next decade, we can seriously consider extending
the spectroscopic comparisons of SNe across redshifts and host
types to higher redshifts than currently available: both the JWST
and ground-based extremely large telescopes (Hook 2013) will
provide relatively easy access to mid-resolution spectroscopy of
faint targets (m ∼ 26) in the NIR, not practical with current instruments. These facilities will allow us not only to extend the
spectroscopic comparisons of SNe Ia to z = 1.5 and above, but
also to characterise the contamination of the Hubble diagram
across redshifts.
Among spectroscopic diagnostics of the chemical composition of the ejecta, assessing the details of the UV flux around
300 nm restframe is particularly useful to estimate the metallicity of the progenitor (Lentz et al. 2000; Foley & Kirshner 2013).
UV spectroscopic measurements already exist at low redshift
(Maguire et al. 2012), and at z ' 0.6 (e.g. Walker et al. 2012,
and references therein). Extending the redshift range of such
measurements should become possible. In A11 (Sect. 5.2) we
proposed photometric measurements of SN metallicity through
the broadband flux at 250 <
∼λ<
∼ 320 nm restframe. Such measurements allow one to control offsets of the distance modulus
at the 0.01 level. In the surveys we are sketching, the data for
such measurements is available at z ' 0.7 (g band) and again at
z ' 1.6 (i band).
9.3. Colour relations and dust extinction
Although the fact that brightness and colours of supernovae are
related is not debated, the physical source of this relation is still
unclear. There are clear signatures of dust extinction in spectra of highly reddened events (e.g. Blondin et al. 2009 and Wang
et al. 2009 and references therein), and some indications that part
of the brighter-bluer relation could be intrinsic to supernovae
(e.g. Foley & Kasen 2011). An intriguing observation is that the
colour distributions seem similar across environments (Sullivan
et al. 2010; Lampeitl et al. 2010), although one would expect
less extinction in passive galaxies than in active ones. Smith
et al. (2012) even provide some indication that supernovae in
passive hosts are slightly redder than in star-forming hosts. It is
thus likely that the observed brighter-bluer relation is a mixture
of dust extinction and intrinsic SN variability. Most of the supernova cosmology analyses eliminate heavily reddened events,
likely to be extincted by dust, because they are rare and faint,
and could be atypical.
Since the brighter-bluer relation is linear in colour vs magnitude space, and different colours are related by linear relations
(e.g. Leibundgut 1988; Conley et al. 2008) it is natural to adopt
the formalism of extinction. In our analysis, we have adopted an
agnostic approach, namely deriving the “extinction law” from
data, without assuming that it belongs to the classical forms determined for dust in the Milky Way (Cardelli et al. 1989). In our
approach, this law is separated in two parts: a polynomial function of wavelength, and the β parameter of Eq. (1). A determination of this law from spectroscopic SN data has shown that it is
a smooth function of wavelength (Chotard et al. 2011), and we
use a polynomial function with 10 coefficients to model it. As
mentioned earlier, if the extinction law and/or the β parameter
have to be determined separately for different event classes, the
impact on the cosmological precision is either very small (A11)
or even null in some cases (A11 Appendix C).
A80, page 16 of 20
The case for a β parameter evolving with redshift is unclear
(see e.g. the discussions in Kessler et al. 2009 and Conley et al.
2011). As in A11, we follow an agnostic route and evaluate the
extra cost of fitting different β values in redshift bins: we find that
fitting separate α and β parameters in ∆z = 0.1 bins decreases the
FoM by less than 1.
10. Other science with DESIRE
While the primary motivation for the DESIRE survey is precision cosmology with distant SNe Ia, the resulting images will
enable a wealth of other science, both using the time series of
images and using the final deep stacked images, from the bands
aimed at measuring distances, but also from the sharp Euclid visible images which can be acquired simultaneously. It is beyond
the scope of the present paper to explore in detail all the possible scientific legacy of DESIRE, but we will just mention a few
examples.
10.1. Transient astrophysics
The large statistics of distant SNe Ia can be used to measure
their rate evolution as a function of redshift. When compared to
the cosmic star formation history (SFH), the rate evolution with
redshift sets strong constraints on the Delay Time Distribution
(DTD) of SNe Ia, and therefore provides information on their
progenitors (e.g. Perrett et al. 2012; Maoz & Mannucci 2012;
Maoz et al. 2014; Graur & Maoz 2013). This analysis will benefit from the comparison with the large transient statistics now
available for the local Universe that is the harvest of a number of
very successful SN searches, e.g. the Palomar Transient Factory
(Rau et al. 2009) or the Catalina Real-Time Transient Survey
(Drake et al. 2012).
Additional constraints on the progenitors scenario (Maoz
et al. 2014) can be obtained by comparing the SNe Ia rates with
the properties of the parent galaxies as obtained from broadband photometry (e.g. Mannucci et al. 2005, 2006; Sullivan et al.
2006; Li et al. 2011) or spectroscopy (Maoz et al. 2012). Besides
the astrophysical interest, this analysis is important for the cosmological use of SNe Ia because it can help to control the systematics related to a possible evolution of these standard candles.
As well as SNe Ia, the DESIRE survey will discover
>1000 core-collapse SNe that can also be used as cosmological
distance indicators. In particular, Hamuy & Pinto (2002) found
a tight correlation between the expansion velocity and plateau
magnitude for II-Plateau SNe (IIP), which has since been extended to cosmologically useful redshifts (Nugent et al. 2006).
Although fainter than SNe Ia, their progenitors are well understood and there is excellent potential for IIP to be used as complementary probes of the cosmological parameters in the NIR
(Maguire et al. 2010).
In addition, the statistics of core collapse events can be used
as an independent probe of the cosmic SFH (e.g. Dahlen et al.
2012) or, if this is known from other estimators, constrain the
stellar initial mass function along with the mass range for core
collapse SN progenitor (e.g. Botticella et al. 2008). There have
been claims of a mismatch between the current estimate of the
SFH and the observed rate of core collapse SNe that needs to be
investigated further (Horiuchi et al. 2011). A proposed explanation is that a large fraction of core collapse SNe remains hidden
in particular in the very dusty nuclear regions of starburst galaxies (Mannucci et al. 2007) and correcting for these (e.g. Mattila
et al. 2012) can lead to core-collapse SN rates consistent with
the expectations from the cosmic SFH (Dahlen et al. 2012).
P. Astier et al.: Distances to high redshift supernovae with Euclid
In this respect a NIR SN search with Euclid is attractive because of the reduced effect of dust extinction that will allow us to
derive a more complete census of all types of SNe (e.g. Maiolino
et al. 2002; Mannucci et al. 2003). It has been shown that the bias
in observed rates due to dust extinction is expected to increase
with redshift even for SNe Ia (e.g. Mannucci et al. 2007; Mattila
et al. 2012 and references therein) and can be a dominant factor
above z ∼ 1.
While the most heavily extinguished SNe will remain out of
reach even for Euclid, the DESIRE survey will allow the detection of a large population of intermediate extinction SNe which
current optical searches mostly miss. All together, DESIRE will
significantly increase the number of core collapse SNe in the
highest redshift bins which are not well sampled now.
Finally, we stress that for the purpose of collecting transient
statistics, parallel observations with the Euclid optical channel
(VIS) would be very valuable. With the combination of IR filters
and optical (unfiltered) monitoring, DESIRE will provide detections, as well as light and colour curves that can be used for
the transient photometric classification and therefore extended
ground based follow-up is not required for this purpose.
Aside from SNe, the DESIRE project will provide a unique
database for the study of active galactic nucleus (AGN) variability. This can be used to identify AGN, in particular those
of fainter magnitude that are more difficult to detect with other
methods, and hence probe the evolution of the faint end of the
AGN luminosity function up to high redshifts (e.g. Sarajedini
et al. 2011). At the same time the data will contribute to our
understanding the physics of AGN variability in the IR spectral window. It has also been proposed that the detailed AGN
light curves may allow reverberation mapping measurements
of AGN/QSO/SuperEddington accreting massive Balck Holes.
Those are currently being studied as possible “standard candles”
that could extend to larger redshifts the range provided by SNe Ia
for measuring distances (e.g. Kaspi et al. 2005; Watson et al.
2011; Bentz et al. 2013; Marziani & Sulentic 2014; Wang et al.
2013a).
10.2. The DESIRE ultra deep field
By the end of the DESIRE survey, an area of 10 deg2 will
have been imaged 90 times, giving a final stacked depth of 28
to 28.5 mag (AB, 5 sigma point source limit) in i, z, y, J and
H bands.
Such an “Ultra-deep field” would make a unique legacy, being about 2 mag deeper than the Euclid Deep survey (40 deg2
reaching AB = 26) while JWST will reach deeper limits but
on a much smaller area (its survey capability is constrained by
NIRCAMs FoV of 2.2 × 4.4 arcmin2 , simultaneously observed
in two bands). Examples of uses for such data include very high
redshift (z > 8) galaxy and QSO surveys going approximately
two magnitudes fainter down the luminosity function than the
baseline Euclid Deep surveys described in Laureijs et al. (2011).
We also note that the spectroscopic SNe Ia host sample that
would be obtained as part of DESIRE will provide calibration
of deep photometric redshifts within this ultra-deep Euclid field,
which will be of lasting legacy value.
Although Euclid VIS data is not used in the SN light curve
analysis (because of its broad wavelength range), the high spatial resolution imaging of VIS would be a powerful complement. If the VIS imager were allowed to integrate while the
NIR DESIRE images are collected, the resulting stacked VIS
image would reach R ∼ 28 (5 sigma for an extended source of
0.300 FWHM). Such deep and sharp Euclid VIS images would
allow deep morphological studies of galaxies in the field (for
which matching depth multicolour data would also be available, see above). Using the several hundred dithered exposures
of the field, the resulting stack can afford a finer pixelisation
than the instrument 0.100 /pixel scale. Such a deep stack would
enable measurement of the location of transients within their
hosts, providing information on possible progenitor scenarios.
In the case of SNe Ia, the position within the host has been
found to correlate with photometric and spectroscopic properties
of the SNe themselves (Wang et al. 1997; Wang et al. 2013b),
which may yield further improvements on cosmological parameter constraints.
11. Summary
We have simulated a high-statistics SN Ia Hubble diagram which
consists of three surveys, which in turn cover the whole redshift
range from z ∼ 0 to z = 1.55. The high-redshift part relies on
deep NIR imaging from Euclid and concurrent observations in
i and z bands from the ground, which consist of monitoring the
same 10 deg2 footprint for two seasons of 6 months each. During
each season, Euclid observes the fields approximately half of the
time, so the total survey time on Euclid amounts to 6 months
(including ∼40% overheads).
We have placed sufficiently stringent observing quality requirements so that all surveys are effectively redshift-limited. We
have assumed that the systematic calibration uncertainties are
0.01 mag (i.e. about two times larger than current achievements),
we have included a correlated irreducible distance modulus uncertainty to account for possible evolution systematics of the
SN population with redshift, and accounted for both statistical
and systematic uncertainties of the SN model used to fit the light
curves. Despite these conservative assumptions, we find that this
large scale Hubble diagram, when combined with a 1D Planck
geometrical prior, can deliver stringent purely geometrical dark
energy constraints: a static equation of state is constrained to
σ(w) = 0.022. We find that the anticipated performance is fairly
robust to changing the assumptions on the size of the leading systematic uncertainties. DESIRE is therefore an exciting prospect
for cosmology, providing significant constraints on dark energy
that are independent of Euclid’s other probes, while the resulting ultra-deep NIR imaging would enable a wealth of Legacy
science.
Acknowledgements. We are grateful to the anonymous referee for suggesting
subtantial improvements to the original manuscript. E.C., S.S. and M.T. acknowledge the grants ASI n.I/023/12/0 Attivit relative alla fase B2/C per la missione Euclid and MIUR PRIN 2010−2011 “The dark Universe and the cosmic
evolution of baryons: from current surveys to Euclid”.
Appendix A: Simulating point source photometry
uncertainties
In order to simulate the precision of SN observations, we have
to derive the flux measurement uncertainty from the value of
the source flux, the instrument characteristics, and the observing conditions. For a point source (SNe are point sources) the
expected content of a pixel pi reads:
pi = f ψi + (d + s)T
where f is the object flux, ψi the PSF at pixel i (i.e. the fraction
of the object flux in this pixel), d is the dark current per pixel, s
is the sky background per pixel per unit time, and T is the exposure time. The flux of a supernova is obtained by integrating the
A80, page 17 of 20
A&A 572, A80 (2014)
(redshifted) SN spectrum in the bandpass of the instrument, accounting for the distance. Expressing all quantities in electrons,
the variance reads:
Vi = f ψi + (d + s)T + r2
where r is the rms read noise and the other terms are just Poisson
variance. A least-squares fit of f to the image should minimise:
X
χ2 =
Ii − pi 2 /Vi
i
where Ii are the measured pixel flux values. The flux estimator
reads:
P
Ii ψi /Vi
fˆ = Pi 2
i ψi /Vi
and its variance:
1
Var( fˆ) = P 2 ·
ψ
i i /Vi
This flux variance is statistically optimal and it is the expression
we use in our simulator. How Vi depends on the object flux determines how Var( fˆ) behaves at the bright and faint ends. At large
flux, Var( fˆ) → f , as expected from Poisson statistics. Faint
sources are those for which sky and dark current dominate the
variance. In this regime, the pixel variance becomes stationnary
(vi ≡ v = Vi = (d + s)T + r2 ), and the flux variance reads:
Var( fˆ) = v P
1
·
2
i ψi d
The rightmost factor has the dimension of an area (expressed in
number of pixels) and is often called the noise equivalent area
(NEA). It summarises the PSF quality for photometry of point
sources:
1
,
2
i ψi
NEA = P
(A.1)
P
with i ψi = 1. This expression accounts for pixelisation, and
is always larger than 1 pixel. For a well sampled Gaussian, the
noise equivalent area reads 4πσ2 , where σ is expressed in pixels.
The NEA values for the Euclid bands are provided (in arcsec2 ) in
Table 1. The Euclid NIR imager is sufficiently coarsely sampled
for the NEA to vary with the source position within a pixel by 10
to 20% rms. Our simulator makes use of a single position that
delivers a NEA representative of the average.
One might note that the above arguments ignore that, in
PSF photometry, one usually has to fit for both position and flux.
However, for an even PSF function, position and flux are uncorrelated, and fitting the position together with the flux does not
degrade the flux variance.
The algebra above applies to measurements in a single image, while supernova photometry requires to subtract an image
of the field without the supernova (deemed “reference image”).
The impact of this subtraction is discussed in the next appendix.
Appendix B: Evaluating the influence of a finite
reference image depth
The fluxes of a supernova are obtained by subtracting supernovafree images from images sampling the light curve. Since the
same supernova-free image (or image set) is subtracted from all
A80, page 18 of 20
SN epochs, the inferred supernovae fluxes are statistically correlated by the noise on these supernovae-free images, deemed
reference. The SN fluxes fiSN (where i indexes epochs) can be
written as:
fiSN = fi − fref
where fi is the flux in image i and fref is the flux measured (at the
same position) on the reference image. The covariance matrix of
SN fluxes reads
Ci j ≡ Cov( fiSN , f jSN ) = δi j Var( fi ) + σ2ref
with σ2ref ≡ Var( fref ). In matrix notation:
W ≡ C −1 = (D + σ2ref 11T )−1 = D−1 − σ2ref
(D−1 1)(D−1 1)T
1 + σ2ref 1T D−1 1
where Di j ≡ δi j Var( fi ), 1 is just a vector filled with 1’s, and we
have made use of the Woodbury matrix identity. Modern differential photometry techniques (e.g. Holtzman et al. 2008) do not
explicitly subtract a reference image, but instead fit a model to
images both with and without the supernova, but this does not
change the structure of the output SN flux covariance matrix.
The measurements fi are used to fit the light curve parameters θ by minimising
χ2 = [Aθ − F]T W[Aθ − F],
where F ≡ ( f1SN , . . . , fnSN ) and Aθ = E[F] (E[X] denotes the
expectation value of the random variable X). The inverse covariance matrix of estimated parameters reads
P
P
T
X
i wi hi i wi hi
T
2
−1
T
wi hi hi − σref
Cθ̂ = A WA =
,
(B.1)
P
1 + σ2ref i wi
i
≡
where hi are the rows of A (i.e. hi = ∂E[ fiSN ]/∂θ), w−1
i
Var( fiSN ), and sums run over the considered measurements. We
use this expression to account for finite reference depth. For an
amplitude parameter a in a single band (i.e. all light curve points
scale with a), we have hi (a) ∝ E[ fi ] ≡ φi , so that the variance of
â, with other parameters fixed, reads
"
#−1 X
P
2
Var(â)
i wi φi
2
2
w
φ
−
σ
=
,
P
i
i
ref
a2
1 + σ2ref i wi
i
where the second term is the contribution of the finite reference
depth.
Appendix C: Supernovae in the Euclid deep field(s)
In this section we study the reach of repeated Euclid standard
visits regarding distances to SNe Ia. In the Euclid wide field
survey, NIR photometry is primarily aimed at securing photometric redshifts of galaxies. This is turned into the requirement
mAB = 24 point sources are measured at 5σ in each of the three
NIR bands, fulfilled by the NIR photometry from a Euclid “standard visit” in the wide survey (Laureijs et al. 2011). The Euclid
deep survey is constructed from repeated standard visits of the
same fields, 40 visits being the baseline, both to increase depth
and for calibration purposes. The latter impose that the observation sequence be exactly the same as in the wide survey.
Following the adopted way to evaluate depth for the Euclid
wide survey, we simulated three exposures of 79, 81 and 48 s
each in the y, J and H bands respectively as a “standard visit”.
0.08
Peak AB mag
sig(fitted peak magnitude)
P. Astier et al.: Distances to high redshift supernovae with Euclid
1-day cadence standard visit
H
0.06
J
0.04
25
24
H
J
y
23
22
0.02
y
21
0
0.2
0.4
0.6
0.8
1
z
0.5
1
z
Fig. C.1. Precisions of the fitted amplitude of light curves with a oneday cadence of standard visits, as a function of redshift. The requirement of 0.04 is met at z <∼ 1 in y and J, and z < 0.5 in H.
Fig. D.1. Average peak AB magnitude of SNe Ia observed in the Euclid
bands as a function of their redshift, in a flat ΛCDM model, as predicted
by our SaltNIR model, trained on nearby multi-band SN Ia events from
Contreras et al. (2010).
The visits indeed acquire four of these images, but the envisaged
dithers between these four exposures are such that most of the
covered sky area indeed only has three exposures.
We simulated supernovae observed with a one-day cadence
which is probably the fastest possible cadence, and find that the
precision of light curve amplitudes is below 0.04 mag up to redshifts of ∼1, 0.9 and 0.5 for y, J and H respectively, as shown in
Fig. C.1. Unfortunately, H being the reddest band, it is most useful at the high end of the redshift interval, as we aim at covering
the same restframe spectral range at all redshifts. These SN simulations require to model SNe at wavelengths redder than what
SALT2 covers and we have assembled for these simulations a
SN Ia model in the NIR described in Appendix D.
This one-day cadence would allow us to survey about
10 deg2 , if exclusively observing this area, at least for some period of time. Optimistically assuming that we operate the oneday cadence over 6 months (i.e. visiting the fields 180 times
rather than 40 times as currently envisioned), and integrating
events up to z = 1 (which marginally meets our quality requirements), we would collect about 500 SN Ia events, i.e. only about
what SNLS collected.
We hence believe that the Euclid deep fields will not deliver
data that allows one to measure a compelling set of SN distances,
even considering a number of visits far above the Euclid current
plans.
predicted by this model in Euclid bands are shown in Fig. D.1
and available in computer-readable form6 .
Appendix E: Material for SN-only forecasts
We here provide the distance constraints that the proposed observing sketch could deliver, including all statistical correlations. This can be combined with other probes as desired. We
parametrise the distance-redshift relation as linear piecewise relation parametrised at equidistant pivot points zi = δz ∗ i, with
i = 0...N. We define di ≡ H0 dM (zi )/c and linearly interpolate
distance values between the pivot points. dM refers to the proper
motion distance:
!
Z z
p
c
dz0
dM (z) =
Sin |Ωk |
√
0
H0 |Ωk |
0 H(z )
where Sin(x) = sinh(x), x, sin(x) according to the sign of the
curvature. The di values define the cosmology (or more precisely
the distance-redshift relation), except for the two first ones, for
which we impose d0 = 0 and d1 = δz. We provide the inverse of
the covariance matrix of the di (i > 2) parameters obtained from
SNe alone, marginalised over all nuisance parameters.
Given an isotropic cosmological model that defines the
proper motion distance dmod (z; θ) as a function of some cosmological parameters θ, we define the residuals to some fiducial
cosmology θ0 as:
Ri = dmod (zi+2 ; θ) − dmod (zi+2 ; θ0 )
Appendix D: SN Ia model in the rest-frame NIR
Since at low redshift, NIR bands address redder restframe spectral regions than those covered by SALT2, we developed a simple SN model designed to deliver realistic amplitudes and light
curve shapes up to almost 2 microns in the rest frame, following the SALT model strategy Guy et al. (2005). It consists of
optimising broadband corrections to an empirical spectral series in order to reproduce a set of training light curves. Our
“SaltNIR” model makes use of the E. Hsiao spectral SN template (Hsiao et al. 2007), with broadband corrections derived
using the first release of low-redshift events from the Carnegie
Supernova Project (Contreras et al. 2010). The wavelength restframe coverage is [330, 1800] nm for the central wavelengths of
the simulated filters. The training data set misses the restframe
z-band which hence consists of the spectral template corrected
by interpolations between i and Y bands. The peak brightnesses
(E.1)
where the lowest index of R is 0. Distances should be understood
here as dimensionless, i.e. H0 dM /c. The least-squares constraints
expected from SNe around the θ0 model simply read:
χ2 = RT WR
(E.2)
where W is the matrix we provide in computer-readable format7 .
This SN χ2 can then be added to χ2 from other probes to obtain
overall cosmology constraints.
We have checked that with δz = 0.025, the cosmological
constraints (with our CMB prior) computed directly and going
through this binned distance scheme agree to better than 1%.
With δz = 0.025, there are 63 control points from z = 0 to z =
1.55, and we provide a matrix of dimension 61, omitting the first
6
7
http://supernovae.in2p3.fr/~astier/desire-paper/
http://supernovae.in2p3.fr/~astier/desire-paper/
A80, page 19 of 20
A&A 572, A80 (2014)
two points as explained above. To generate this matrix, we used a
flat ΛCDM model with ΩM = 0.27, but the current uncertainties
of the distance-redshift relation should not require to alter this
W matrix for cosmologies that yield a realistic distance-redshift
relation.
References
Albrecht, A., Bernstein, G., Cahn, R., et al. 2006 [arXiv:astro-ph/0609591]
Albrecht, A., Amendola, L., Bernstein, G., et al. 2009 [arXiv:0901.0721]
Amati, L., & Valle, M. D. 2013, Int. J. Mod. Phys. D, 22, 30028
Amendola, L., Appleby, S., Bacon, D., et al. 2013, Liv. Rev. Relat., 16, 6
Astier, P., Guy, J., Regnault, N., et al. 2006, A&A, 447, 31
Astier, P., Guy, J., Pain, R., & Balland, C. 2011, A&A, 525, A7
Astier, P., El Hage, P., Guy, J., et al. 2013, A&A, 557, A55
Balland, C., Baumont, S., Basa, S., et al. 2009, A&A, 507, 85
Bazin, G., Ruhlmann-Kleider, V., Palanque-Delabrouille, N., et al. 2011, A&A,
534, A43
Bean, R., Bernat, D., Pogosian, L., Silvestri, A., & Trodden, M. 2007,
Phys. Rev. D, 75, 064020
Bentz, M. C., Denney, K. D., Grier, C. J., et al. 2013, ApJ, 767, 149
Bernardeau, F., & Brax, P. 2011, J. Cosmol. Astropart. Phys., 6, 19
Bernstein, J. P., Kessler, R., Kuhlmann, S., et al. 2012, ApJ, 753, 152
Betoule, M., Marriner, J., Regnault, N., et al. 2013, A&A, 552, A124
Betoule, M., Kessler, R., Guy, J., et al. 2014, A&A, 568, A22
Blake, C., Kazin, E. A., Beutler, F., et al. 2011, MNRAS, 418, 1707
Blondin, S., Prieto, J. L., Patat, F., et al. 2009, ApJ, 693, 207
Blondin, S., Matheson, T., Kirshner, R. P., et al. 2012, AJ, 143, 126
Botticella, M. T., Riello, M., Cappellaro, E., et al. 2008, A&A, 479, 49
Boulade, O., Charlot, X., Abbon, P., et al. 2003, in Instrument Design and
Performance for Optical/Infrared Ground-based Telescopes, eds. M. Iye, &
A. F. M. Moorwood, Proc. SPIE, 4841, 72
Burenin, R. A., & Vikhlinin, A. A. 2012, Astron. Lett., 38, 347
Campbell, H., D’Andrea, C. B., Nichol, R. C., et al. 2013, ApJ, 763, 88
Cardelli, J. A., Clayton, G. C., & Mathis, J. S. 1989, APJ, 345, 245
Chevallier, M., & Polarski, D. 2001, Int. J. Mod. Phys. D, 10, 213
Childress, M., Aldering, G., Antilogus, P., et al. 2013, ApJ, 770, 108
Chotard, N., Gangler, E., Aldering, G., et al. 2011, A&A, 529, L4
Conley, A., Sullivan, M., Hsiao, E. Y., et al. 2008, ApJ, 681, 482
Conley, A., Guy, J., Sullivan, M., et al. 2011, ApJS, 192, 1
Contreras, C., Hamuy, M., Phillips, M. M., et al. 2010, AJ, 139, 519
Dahlen, T., Strolger, L.-G., Riess, A. G., et al. 2012, ApJ, 757, 70
D’Andrea, C. B., Gupta, R. R., Sako, M., et al. 2011, ApJ, 743, 172
Drake, A. J., Djorgovski, S. G., Mahabal, A., et al. 2012, in IAU Symp. 285, eds.
E. Griffin, R. Hanisch, & R. Seaman, 306
Flaugher, B. L., Abbott, T. M. C., Annis, J., et al. 2010, in SPIE Conf. Ser., 7735
Foley, R. J., & Kasen, D. 2011, ApJ, 729, 55
Foley, R. J., & Kirshner, R. P. 2013, ApJ, 769, L1
Graur, O., & Maoz, D. 2013, MNRAS, 430, 1746
Graur, O., Poznanski, D., Maoz, D., et al. 2011, MNRAS, 417, 916
Graur, O., Rodney, S. A., Maoz, D., et al. 2014, ApJ, 783, 28
Green, J., Schechter, P., Baltay, C., et al. 2012 [arXiv:1208.4012]
Gupta, R. R., D’Andrea, C. B., Sako, M., et al. 2011, ApJ, 740, 92
Guy, J., Astier, P., Nobili, S., Regnault, N., & Pain, R. 2005, A&A, 443, 781
Guy, J., Astier, P., Baumont, S., et al. 2007, A&A, 466, 11
Guy, J., Sullivan, M., Conley, A., et al. 2010, A&A, 523, A7
Hamuy, M., & Pinto, P. A. 2002, ApJ, 566, L63
Hayden, B. T., Gupta, R. R., Garnavich, P. M., et al. 2013, ApJ, 764, 191
Hicken, M., Challis, P., Kirshner, R. P., et al. 2012, ApJS, 200, 12
Holtzman, J. A., Marriner, J., Kessler, R., et al. 2008, AJ, 136, 2306
Hook, I. M. 2013, Roy. Soc. Lond. Philosoph. Trans. Ser. A, 371, 20282
Horiuchi, S., Beacom, J. F., Kochanek, C. S., et al. 2011, ApJ, 738, 154
Howell, D. A., Sullivan, M., Perrett, K., et al. 2005, ApJ, 634, 1190
Hsiao, E. Y., Conley, A., Howell, D. A., et al. 2007, ApJ, 663, 1187
Ivezic, Z., Tyson, J. A., Acosta, E., et al. 2008 [arXiv:0805.2366]
Kaspi, S., Maoz, D., Netzer, H., et al. 2005, ApJ, 629, 61
Keller, S. C., Schmidt, B. P., Bessell, M. S., et al. 2007, PASA, 24, 1
Kelly, P. L., Hicken, M., Burke, D. L., Mandel, K. S., & Kirshner, R. P. 2010,
ApJ, 715, 743
Kessler, R., Becker, A. C., Cinabro, D., et al. 2009, ApJS, 185, 32
Kessler, R., Cinabro, D., Bassett, B., et al. 2010, ApJ, 717, 40
Kessler, R., Guy, J., Marriner, J., et al. 2013, ApJ, 764, 48
Kim, A. G., & Miquel, R. 2006, Astropart. Phys., 24, 451
Lampeitl, H., Smith, M., Nichol, R. C., et al. 2010, ApJ, 722, 566
Laureijs, R., Amiaux, J., Arduini, S., et al. 2011 [arXiv:1110.3193]
A80, page 20 of 20
Law, N. M., Kulkarni, S. R., Dekany, R. G., et al. 2009, PASP, 121, 1395
Le Fevre, O., Tasca, L. A. M., Cassata, P., et al. 2014, A&A, submitted
[arXiv:1403.3938]
Leibundgut, B. 1988, Ph.D. Thesis, Univ. Basel., Switzerland
Leinert, C., Bowyer, S., Haikala, L. K., et al. 1998, A&AS, 127, 1
Lentz, E. J., Baron, E., Branch, D., Hauschildt, P. H., & Nugent, P. E. 2000, ApJ,
530, 966
Li, W., Chornock, R., Leaman, J., et al. 2011, MNRAS, 412, 1473
Lidman, C., Ruhlmann-Kleider, V., Sullivan, M., et al. 2013, PASA, 30, 1
Linder, E. V. 2003, Phys. Rev. Lett., 90, 091301
Linder, E. V. 2005, Phys. Rev. D, 72, 043529
Lue, A., Scoccimarro, R., & Starkman, G. D. 2004, Phys. Rev. D, 69, 124015
Maguire, K., Kotak, R., Smartt, S. J., et al. 2010, MNRAS, 403, L11
Maguire, K., Sullivan, M., Ellis, R. S., et al. 2012, MNRAS, 426, 2359
Maiolino, R., Vanzi, L., Mannucci, F., et al. 2002, A&A, 389, 84
Mannucci, F., Maiolino, R., Cresci, G., et al. 2003, A&A, 401, 519
Mannucci, F., Della Valle, M., Panagia, N., et al. 2005, A&A, 433, 807
Mannucci, F., Della Valle, M., & Panagia, N. 2006, MNRAS, 370, 773
Mannucci, F., Della Valle, M., & Panagia, N. 2007, MNRAS, 377, 1229
Maoz, D., & Mannucci, F. 2012, PASA, 29, 447
Maoz, D., Mannucci, F., & Brandt, T. D. 2012, MNRAS, 426, 3282
Maoz, D., Mannucci, F., & Nelemans, G. 2014, ARA&A, 52, 107
Marziani, P., & Sulentic, J. W. 2014, Adv. Space Res., 54, 1331
Mattila, S., Dahlen, T., Efstathiou, A., et al. 2012, ApJ, 756, 111
Miyazaki, S., Komiyama, Y., Nakaya, H., et al. 2012, in SPIE Conf. Ser., 8446
Mukherjee, P., Kunz, M., Parkinson, D., & Wang, Y. 2008, Phys. Rev. D, 78,
083529
Nugent, P., Sullivan, M., Ellis, R., et al. 2006, ApJ, 645, 841
Palanque-Delabrouille, N., Ruhlmann-Kleider, V., Pascal, S., et al. 2010, A&A,
514, A63
Pan, Y.-C., Sullivan, M., Maguire, K., et al. 2013, MNRAS
Peacock, J. A., Schneider, P., Efstathiou, G., et al. 2006, ESA-ESO Working
Group on Fundamental Cosmology, Tech. Rep.
Perlmutter, S., Aldering, G., Goldhaber, G., et al. 1999, ApJ, 517, 565
Perrett, K., Balam, D., Sullivan, M., et al. 2010, AJ, 140, 518
Perrett, K., Sullivan, M., Conley, A., et al. 2012, AJ, 144, 59
Planck Collaboration XVI. 2014, A&A, 571, A16
Rau, A., Kulkarni, S. R., Law, N. M., et al. 2009, PASP, 121, 1334
Regnault, N., Conley, A., Guy, J., et al. 2009, A&A, 506, 999
Rest, A., Scolnic, D., Foley, R. J., et al. 2014, ApJ, 795, 44
Riess, A. G., Filippenko, A. V., Challis, P., et al. 1998, AJ, 116, 1009
Riess, A. G., Strolger, L., Tonry, J., et al. 2004, ApJ, 607, 665
Riess, A. G., Strolger, L.-G., Casertano, S., et al. 2007, ApJ, 659, 98
Riess, A. G., Macri, L., Casertano, S., et al. 2011, ApJ, 730, 119
Ripoche, P. 2008, Moriond Proceedings (Cosmology)
Rodney, S. A., Riess, A. G., Dahlen, T., et al. 2012, ApJ, 746, 5
Rodney, S. A., Riess, A. G., Strolger, L.-G., et al. 2014, AJ, 148, 13
Rubin, D., Knop, R. A., Rykoff, E., et al. 2013, ApJ, 763, 35
Sako, M., Bassett, B., Connolly, B., et al. 2011, ApJ, 738, 162
Sako, M., Bassett, B., Becker, A. C., et al. 2014, ApJS, submitted
[arXiv:1401.3317]
Sarajedini, V. L., Koo, D. C., Klesman, A. J., et al. 2011, ApJ, 731, 97
Schlegel, D. J., Bebek, C., Heetderks, H., et al. 2009 [arXiv:0904.0468]
Schmidt, B. P., Suntzeff, N. B., Phillips, M. M., et al. 1998, ApJ, 507, 46
Schrabback, T., Hartlap, J., Joachimi, B., et al. 2010, A&A, 516, A63
Scolnic, D., Rest, A., Riess, A., et al. 2014a, ApJ, 795, 45
Scolnic, D. M., Riess, A. G., Foley, R. J., et al. 2014b, ApJ, 780, 37
Silverman, J. M., Foley, R. J., Filippenko, A. V., et al. 2012, MNRAS, 425, 1789
Smith, M., Nichol, R. C., Dilday, B., et al. 2012, ApJ, 755, 61
Spergel, D., Gehrels, N., Breckinridge, J., et al. 2013 [arXiv:1305.5422]
Stritzinger, M. D., Phillips, M. M., Boldt, L. N., et al. 2011, AJ, 142, 156
Sullivan, M., Le Borgne, D., Pritchet, C. J., et al. 2006, ApJ, 648, 868
Sullivan, M., Conley, A., Howell, D. A., et al. 2010, MNRAS, 406, 782
Sullivan, M., Guy, J., Conley, A., et al. 2011, ApJ, 737, 102
Suzuki, N., Rubin, D., Lidman, C., et al. 2012, ApJ, 746, 85
Tripp, R., & Branch, D. 1999, ApJ, 525, 209
Walker, E. S., Hachinger, S., Mazzali, P. A., et al. 2012, MNRAS, 427, 103
Wang, L., Hoeflich, P., & Wheeler, J. C. 1997, ApJ, 483, L29
Wang, X., Filippenko, A. V., Ganeshalingam, M., et al. 2009, ApJ, 699, L139
Wang, J.-M., Du, P., Valls-Gabaud, D., Hu, C., & Netzer, H. 2013a, Phys. Rev.
Lett., 110, 081301
Wang, X., Wang, L., Filippenko, A. V., Zhang, T., & Zhao, X. 2013b, Science,
340, 170
Watson, D., Denney, K. D., Vestergaard, M., & Davis, T. M. 2011, ApJ, 740,
L49
Wood-Vasey, W. M., Miknaitis, G., Stubbs, C. W., et al. 2007, ApJ, 666, 694
Zheng, C., Romani, R. W., Sako, M., et al. 2008, AJ, 135, 1766